494:, is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. A random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, say research subjects, has the same probability of being chosen, then we can say the selection process is random.
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select the other door. Intuitively, one might think the player is choosing between two doors with equal probability, and that the opportunity to choose another door makes no difference. However, an analysis of the probability spaces would reveal that the contestant has received new information, and that changing to the other door would increase their chances of winning.
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likely to come up more often in the future. This logic is valid only if the randomisation might be biased, for example if a die is suspected to be loaded then its failure to roll enough sixes would be evidence of that loading. If the die is known to be fair, then previous rolls can give no indication of future events.
853:'s semi-eponymous definition: An infinite sequence is random if and only if it withstands all recursively enumerable null sets. The other notions of random sequences include, among others, recursive randomness and Schnorr randomness, which are based on recursively computable martingales. It was shown by
1927:
Monroe, J. Grey; Srikant, Thanvi; Carbonell-Bejerano, Pablo; Becker, Claude; Lensink, Mariele; Exposito-Alonso, Moises; Klein, Marie; Hildebrandt, Julia; Neumann, Manuela; Kliebenstein, Daniel; Weng, Mao-Lun; Imbert, Eric; Ă
gren, Jon; Rutter, Matthew T.; Fenster, Charles B.; Weigel, Detlef (February
574:
The formalization of odds and chance was perhaps earliest done by the
Chinese of 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various
1411:
For example, when being told that a woman has two children, one might be interested in knowing if either of them is a girl, and if yes, the probability that the other child is also a girl. Considering the two events independently, one might expect that the probability that the other child is female
1436:
behind the others. Once the contestant has chosen a door, the host opens one of the remaining doors to reveal a goat, eliminating that door as an option. With only two doors left (one with the car, the other with another goat), the player must decide to either keep their decision, or to switch and
1419:
To be sure, the probability space does illustrate four ways of having these two children: boy-boy, girl-boy, boy-girl, and girl-girl. But once it is known that at least one of the children is female, this rules out the boy-boy scenario, leaving only three ways of having the two children: boy-girl,
1377:
In a random sequence of numbers, a number may be said to be cursed because it has come up less often in the past, and so it is thought that it will occur less often in the future. A number may be assumed to be blessed because it has occurred more often than others in the past, and so it is thought
1357:
are drawn and not returned to the deck. In this case, once a jack is removed from the deck, the next draw is less likely to be a jack and more likely to be some other card. However, if the jack is returned to the deck, and the deck is thoroughly reshuffled, a jack is as likely to be drawn as any
2277:
Municipal
Elections Act (Ontario, Canada) 1996, c. 32, Sched., s. 62 (3) : "If the recount indicates that two or more candidates who cannot both or all be declared elected to an office have received the same number of votes, the clerk shall choose the successful candidate or candidates by
1352:
This argument is, "In a random selection of numbers, since all numbers eventually appear, those that have not come up yet are 'due', and thus more likely to come up soon." This logic is only correct if applied to a system where numbers that come up are removed from the system, such as when
759:
Several authors also claim that evolution (and sometimes development) requires a specific form of randomness, namely the introduction of qualitatively new behaviors. Instead of the choice of one possibility among several pre-given ones, this randomness corresponds to the formation of new
973:
ideas of some religions, such as those where the universe is created by an omniscient deity who is aware of all past and future events. If the universe is regarded to have a purpose, then randomness can be seen as impossible. This is one of the rationales for religious opposition to
778:
As far as behavior is concerned, randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories.
876:
Pi certainly seems to behave this way. In the first six billion decimal places of pi, each of the digits from 0 through 9 shows up about six hundred million times. Yet such results, conceivably accidental, do not prove normality even in base 10, much less normality in other number
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due to the systematically improved chance for survival and reproduction that those mutated genes confer on individuals who possess them. The location of the mutation is not entirely random however as e.g. biologically important regions may be more protected from mutations.
725:
is placed in a controlled environment, it cannot be predicted how long it will take for the atom to decayâonly the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments, but only the probabilities.
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evolve at random, in the sense that the expected value of their change is zero but the actual value may turn out to be positive or negative. More generally, asset prices are influenced by a variety of unpredictable events in the general economic environment.
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902:. This allows surveys of completely random groups of people to provide realistic data that is reflective of the population. Common methods of doing this include drawing names out of a hat or using a random digit chart (a large table of random digits).
1387:, so observing outcomes to determine which events are more probable makes sense. However, it is fallacious to apply this logic to systems designed and known to make all outcomes equally likely, such as shuffled cards, dice, and roulette wheels.
413:, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance,
730:
reject the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are at work behind the scenes, determining the outcome in each case.
1313:
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number selection schemes. Truly random processes such as these do not have memory, which makes it impossible for past outcomes to affect future outcomes. In fact, there is no finite number of trials that can guarantee a success.
513:
stated that "given the impossibility of true randomness, the effort is directed towards studying degrees of randomness". It can be proven that there is infinite hierarchy (in terms of quality or strength) of forms of randomness.
1427:
In general, by using a probability space, one is less likely to miss out on possible scenarios, or to neglect the importance of new information. This technique can be used to provide insights in other situations such as the
602:
The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In the mid-to-late-20th century, ideas of
1395:
In the beginning of a scenario, one might calculate the probability of a certain event. However, as soon as one gains more information about the scenario, one may need to re-calculate the probability accordingly.
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wheels, were first developed for use in gambling. The ability to produce random numbers fairly is vital to electronic gambling, and, as such, the methods used to create them are usually regulated by government
721:, microscopic phenomena are objectively random. That is, in an experiment that controls all causally relevant parameters, some aspects of the outcome still vary randomly. For example, if a single unstable
1815:
Zeilinger, Anton; Aspelmeyer, Markus; Ć»ukowski, Marek; Brukner, Äaslav; Kaltenbaek, Rainer; Paterek, Tomasz; Gröblacher, Simon (April 2007). "An experimental test of non-local realism".
424:
The fields of mathematics, probability, and statistics use formal definitions of randomness, typically assuming that there is some 'objective' probability distribution. In statistics, a
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other card. The same applies in any other process where objects are selected independently, and none are removed after each event, such as the roll of a die, a coin toss, or most
1562:
defines "random" as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard."
910:
In information science, irrelevant or meaningless data is considered noise. Noise consists of numerous transient disturbances, with a statistically randomized time distribution.
763:
The characteristics of an organism arise to some extent deterministically (e.g., under the influence of genes and the environment), and to some extent randomly. For example, the
1312:
928:, who said that there were a fixed number of nodes and this number remained fixed for the life of the network, and that all nodes were equal and linked randomly to each other.
1270:, generating large amounts of sufficiently random numbers (which is important in statistics) required a lot of work. Results would sometimes be collected and distributed as
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1031:(equality of political rights), and used complex allotment machines to ensure that the positions on the ruling committees that ran Athens were fairly allocated.
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Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the 20th century computer scientists began to realize that the
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winners. In fact, randomness has been used for games of chance throughout history, and to select out individuals for an unwanted task in a fair way (see
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917:, randomness in a signal is called "noise", and is opposed to that component of its variation that is causally attributable to the source, the signal.
2186:
The distribution of freckles seems entirely random, and not associated with any other obviously punctuate anatomical or physiological feature of skin.
868:. The decimal digits of pi constitute an infinite sequence and "never repeat in a cyclical fashion." Numbers like pi are also considered likely to be
1407:, when the host reveals one door that contains a goat, this provides new information that needs to be factored into the calculation of probabilities.
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to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has
5305:
1993:
Belfield, Eric J.; Ding, Zhong Jie; Jamieson, Fiona J.C.; Visscher, Anne M.; Zheng, Shao Jian; Mithani, Aziz; Harberd, Nicholas P. (January 2018).
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and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known
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996:. As such, this conception is at odd with the idea of randomness, and any reconciliation between both of them would require an explanation.
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Longo, Giuseppe; Montévil, Maël; Kauffman, Stuart (1 January 2012). "No entailing laws, but enablement in the evolution of the biosphere".
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suggested that "while disorder is more probable in general, complete disorder is impossible". Misunderstanding this can lead to numerous
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zero. Consistent non-convergence is thus evidence of the lack of a fixed probability distribution, as in many evolutionary processes.
501:, pure randomness (in the sense of there being no discernible pattern) is impossible, especially for large structures. Mathematician
432:. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in
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In most of its mathematical, political, social and religious uses, randomness is used for its innate "fairness" and lack of bias.
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introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such
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is now restricted to selecting jurors in Anglo-Saxon legal systems, and in situations where "fairness" is approximated by
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1296:, or a mixture of these, such as the tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.
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In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw
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girl-boy, girl-girl. From this, it can be seen only â
of these scenarios would have the other child also be a girl (see
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409:, the frequency of different outcomes over repeated events (or "trials") is predictable. For example, when throwing two
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Popular perceptions of randomness are frequently mistaken, and are often based on fallacious reasoning or intuitions.
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It is generally accepted that there exist three mechanisms responsible for (apparently) random behavior in systems:
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In terms of the development of random networks, for communication randomness rests on the two simple assumptions of
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There are many practical measures of randomness for a binary sequence. These include measures based on frequency,
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have led to many different methods for generating random data. These methods may vary as to how unpredictable or
1217:, and is observed in systems whose behavior is very sensitive to small variations in initial conditions (such as
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can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions.
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to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of
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1328:. However, this may follow a scheme which a human could only recognize after a scientific-style supervision.
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has been used to certify the presence of genuine or strong form of randomness in a given string of numbers.
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and the algorithm used. These methods are often quicker than getting "true" randomness from the environment.
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systems. Computational solutions for some types of problems use random numbers extensively, such as in the
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In some religious contexts, procedures that are commonly perceived as randomizers are used for divination.
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that appear on a person's skin is controlled by genes and exposure to light; whereas the exact location of
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arose from attempts to formulate mathematical descriptions of chance events, originally in the context of
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see what appears to be a random event as a means for a divine being to communicate their will (see also
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1432:, a game show scenario in which a car is hidden behind one of three doors, and two goats are hidden as
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philosophies state that any event is the result of previous events, as is reflected in the concept of
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1118:: Random numbers are also employed where their use is mathematically important, such as sampling for
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illustrating all possible outcomes, one would notice that the probability is actually only â
(33%).
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1247:) for generating pseudorandom numbers. The behavior of the system can be determined by knowing the
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In the 19th century, scientists used the idea of random motions of molecules in the development of
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1140:: Random allocation of a clinical intervention is used to reduce bias in controlled trials (e.g.,
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1883:"Each nucleus decays spontaneously, at random, in accordance with the blind workings of chance."
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is random if and only if it is shorter than any computer program that can produce that string (
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Breathnach, A. S. (1982). "A long-term hypopigmentary effect of thorium-X on freckled skin".
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Proceedings of the 14th annual conference companion on
Genetic and evolutionary computation
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page 115. The 1866 edition of Venn's book (on Google books) does not include this chapter.
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elections in some jurisdictions. Its use in politics originates long ago. Many offices in
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had a positive impact on the formal study of randomness. In the 1888 edition of his book
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uses the casting of bones or dice to reveal what is seen as the will of the gods.
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Pironio, S.; et al. (2010). "Random
Numbers Certified by Bell's Theorem".
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Quantum random number generator with single photons as interactive experiment.
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by
Kenneth Chan includes a "Random Scale" for grading the level of randomness.
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The Art of
Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed.
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2010:
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1614:"Complete Disorder is Impossible: The Mathematical Work of Walter Deuber"
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849:. For the notion of infinite sequence, mathematicians generally accept
390:
402:
31:. For information about Knowledge (XXG)'s random article feature, see
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4512:
3763:
3554:
3272:
537:
533:
475:), are important techniques in science, particularly in the field of
428:
is an assignment of a numerical value to each possible outcome of an
398:
379:
2106:
2043:
1901:"Study challenges evolutionary theory that DNA mutations are random"
2553:
2541:
2437:. Academic Press, New York, London; Akademie-Verlag, Berlin, 1986.
27:"Random" redirects here. For a random Knowledge (XXG) article, see
2564:
2341:
2054:
1930:"Mutation bias reflects natural selection in Arabidopsis thaliana"
1829:
1674:
in "The
Incomputable Journeys Beyond the Turing Barrier" Editors:
1309:
1179:
1040:
993:
985:
527:
370:
1995:"DNA mismatch repair preferentially protects genes from mutation"
982:
selection is applied to the results of random genetic variation.
440:
is a sequence of random variables whose outcomes do not follow a
3497:
1222:
1058:
722:
544:
410:
5466:
5033:
4780:
4079:
3849:
3466:
3410:
2591:
2587:
803:
of a collection of empirical observations. For the purposes of
2107:"Extended criticality, phase spaces and enablement in biology"
1381:
In nature, events rarely occur with a frequency that is known
1213:
coming from the initial conditions. This aspect is studied by
822:
3406:
1529:
Strictly speaking, the frequency of an outcome will converge
1263:
they are, and how quickly they can generate random numbers.
829:), which means that random strings are those that cannot be
2565:
A Pseudorandom Number
Sequence Test Program (Public Domain)
2535:
1231:
intrinsically generated by the system. This is also called
1053:: Random numbers were first investigated in the context of
865:
592:
2244:"Are the digits of pi random? researcher may hold the key"
2230:
Yongge Wang: Randomness and
Complexity. PhD Thesis, 1996.
1320:
Due to an electric defect, the shown input selector of an
743:
ascribes the observed diversity of life to random genetic
607:
introduced new dimensions to the field via the concept of
591:
that included his view of the randomness of the digits of
2048:. GECCO '12. New York, NY, US: ACM. pp. 1379â1392.
2547:
1150:: Although not intended to be random, various forms of
857:
that these randomness notions are generally different.
2268:
Laszso
Barabasi, (2003), Linked, Rich Gets Richer, P81
1672:"Quantum Randomness: From Practice to Theory and Back"
1602:, Jun Liu, Professor of Statistics, Harvard University
953:
Random selection can be an official method to resolve
630:
Many scientific fields are concerned with randomness:
2314:
Terry Ritter, Randomness tests: a literature survey.
898:
In statistics, randomness is commonly used to create
551:
to attempt to circumvent randomness and fate. Beyond
448:. These and other constructs are extremely useful in
5319:
Autoregressive conditional heteroskedasticity (ARCH)
1096:
to randomly select starting conditions for games or
42:
Apparent lack of pattern or predictability in events
5626:
5563:
5516:
5479:
5434:
5416:
5383:
5374:
5332:
5279:
5240:
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4499:
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4365:
4291:
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4092:
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3110:
3048:
2918:
2905:
2857:
2788:
2632:
2625:
2511:
The Drunkardâs Walk: How Randomness Rules our Lives
2232:http://webpages.uncc.edu/yonwang/papers/thesis.pdf
2105:Longo, Giuseppe; Montévil, Maël (1 October 2013).
751:. The latter retains some random mutations in the
490:Random selection, when narrowly associated with a
1506:âgenerates random numbers using atmospheric noise
717:According to several standard interpretations of
2544:generates random numbers from radioactive decay.
1738:The Athenian Democracy in the Age of Demosthenes
817:studies, among other topics, what constitutes a
622:even outperform the best deterministic methods.
463:to signify well-defined statistical properties.
4867:Multivariate adaptive regression splines (MARS)
1766:Annotated readings in the history of statistics
969:Randomness can be seen as conflicting with the
874:
444:pattern, but follow an evolution described by
3422:
2603:
1074:. Random drawings are also used to determine
961:were chosen by lot instead of modern voting.
397:in information. A random sequence of events,
352:
8:
1682:, 169â181, doi:10.1007/978-3-319-43669-2_11.
1663:
1661:
940:considers that asset prices in an organized
807:, it is necessary to have a large supply of
1654:The origin of countless conspiracy theories
1576:"Definition of randomness | Dictionary.com"
467:, which rely on random input (such as from
389:is the apparent or actual lack of definite
5476:
5463:
5380:
5186:
5055:
5030:
4801:
4777:
4505:
4288:
4089:
4076:
3859:
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3485:
3476:
3463:
3429:
3415:
3407:
2915:
2629:
2610:
2596:
2588:
2560:Chaitin: Randomness and Mathematical Proof
1367:Fallacy: a number is "cursed" or "blessed"
1199:coming from the environment (for example,
359:
345:
46:
2386:
2384:
2340:
2215:
2063:
2053:
2018:
1969:
1828:
1619:Combinatorics, Probability and Computing
1398:
1057:, and many randomizing devices, such as
795:, but later in connection with physics.
2291:The Law of Karma: A Philosophical Study
2246:. Lbl.gov. 23 July 2001. Archived from
1549:
1522:
821:. The central idea is that a string of
57:
5393:KaplanâMeier estimator (product limit)
2294:. Palgrave Macmillan UK. p. 121.
1239:. There are many algorithms (based on
811:âor means to generate them on demand.
2454:. Reading, MA: Addison-Wesley, 1997.
1600:Third Workshop on Monte Carlo Methods
860:Randomness occurs in numbers such as
7:
5703:
5403:Accelerated failure time (AFT) model
2517:. Pantheon Books, New York, 2008.
2200:"The definition of random sequences"
2113:. Emergent Critical Brain Dynamics.
1626:. Cambridge University Press: 3â16.
1570:
1568:
1306:Misconceptions and logical fallacies
5715:
4998:Analysis of variance (ANOVA, anova)
2750:Measure-preserving dynamical system
2583:Stanford Encyclopedia of Philosophy
1266:Before the advent of computational
559:, randomness has been attested for
5093:CochranâMantelâHaenszel statistics
3719:Pearson product-moment correlation
2571:Dictionary of the History of Ideas
2419:. Harvard University Press, 1998.
2166:10.1111/j.1365-2133.1982.tb00897.x
595:(Ï), by using them to construct a
575:games of chance. The invention of
25:
3318:Oleksandr Mykolayovych Sharkovsky
2556:Fast Quantum Random Bit Generator
1205:hardware random number generators
833:. Pioneers of this field include
459:Randomness is most often used in
5714:
5702:
5690:
5677:
5676:
2848:
2840:
2493:. Springer-Verlag London, 2001.
1692:Handbook to life in ancient Rome
1447:
1122:and for statistical sampling in
65:
5352:Least-squares spectral analysis
2391:Johnson, George (8 June 2008).
1391:Fallacy: odds are never dynamic
1237:pseudo-random number generators
1106:National Basketball Association
799:is used to infer an underlying
4333:Mean-unbiased minimum-variance
3083:RabinovichâFabrikant equations
2154:British Journal of Dermatology
2111:Chaos, Solitons & Fractals
1788:"Concept: Types of algorithms"
1712:Religions of the ancient world
1412:is œ (50%), but by building a
815:Algorithmic information theory
605:algorithmic information theory
485:quasi-random number generators
473:pseudorandom number generators
132:Collectively exhaustive events
1:
5646:Geographic information system
4862:Simultaneous equations models
2217:10.1016/S0019-9958(66)80018-9
1112:to order teams in its draft.
741:modern evolutionary synthesis
4829:Coefficient of determination
4440:Uniformly most powerful test
2550:Quantum Random Bit Generator
1768:by Herbert Aron David, 2001
1714:by Sarah Iles Johnston 2004
1324:switches fast and seemingly
1142:randomized controlled trials
1027:was based on the concept of
589:The conception of randomness
5398:Proportional hazards models
5342:Spectral density estimation
5324:Vector autoregression (VAR)
4758:Maximum posterior estimator
3990:Randomized controlled trial
2818:Poincaré recurrence theorem
2288:Reichenbach, Bruce (1990).
2131:10.1016/j.chaos.2013.03.008
1612:Hans JĂŒrgen Prömel (2005).
1489:Probability interpretations
787:The mathematical theory of
5769:
5158:Multivariate distributions
3578:Average absolute deviation
2813:PoincarĂ©âBendixson theorem
1954:10.1038/s41586-021-04269-6
1370:
1348:Coupon collector's problem
1345:
1342:Fallacy: a number is "due"
1331:
1281:
1257:applications of randomness
1235:, and is the kind used in
1173:
1013:Applications of randomness
1010:
891:
885:
521:
454:applications of randomness
26:
5672:
5475:
5462:
5146:Structural equation model
5054:
5029:
4800:
4776:
4508:
4482:Score/Lagrange multiplier
4088:
4075:
3897:Sample size determination
3858:
3845:
3475:
3462:
3444:
3165:Swinging Atwood's machine
2838:
2808:KrylovâBogolyubov theorem
2685:
1632:10.1017/S0963548304006674
1559:Oxford English Dictionary
1088:: Some sports, including
481:quasi-Monte Carlo methods
446:probability distributions
5641:Environmental statistics
5163:Elliptical distributions
4956:Generalized linear model
4885:Simple linear regression
4655:HodgesâLehmann estimator
4112:Probability distribution
4021:Stochastic approximation
3583:Coefficient of variation
3073:LotkaâVolterra equations
2897:Synchronization of chaos
2700:axiom A dynamical system
2579:Chance versus Randomness
2475:. Thomson Texere, 2004.
2431:Random Measures, 4th ed.
2198:Martin-Löf, Per (1966).
1795:Freie UniversitÀt Berlin
1268:random number generators
1176:Random number generation
801:probability distribution
728:Hidden variable theories
706:to explain phenomena in
698:In the physical sciences
469:random number generators
407:probability distribution
377:pseudorandomly generated
302:Law of total probability
297:Conditional independence
186:Exponential distribution
171:Probability distribution
5301:Cross-correlation (XCF)
4909:Non-standard predictors
4343:LehmannâScheffĂ© theorem
4016:Adaptive clinical trial
3058:Double scroll attractor
2823:Stable manifold theorem
2730:False nearest neighbors
2204:Information and Control
2074:10.1145/2330784.2330946
1474:Frequentist probability
1469:Chance (disambiguation)
1063:shuffling playing cards
965:Randomness and religion
775:freckles seems random.
712:the properties of gases
636:Algorithmic probability
563:since at least ancient
281:Conditional probability
37:Random (disambiguation)
5753:Statistical randomness
5697:Mathematics portal
5518:Engineering statistics
5426:NelsonâAalen estimator
5003:Analysis of covariance
4890:Ordinary least squares
4814:Pearson product-moment
4218:Statistical functional
4129:Empirical distribution
3962:Controlled experiments
3691:Frequency distribution
3469:Descriptive statistics
3098:Van der Pol oscillator
3078:MackeyâGlass equations
2710:Box-counting dimension
1786:Reinert, Knut (2010).
1694:by Lesley Adkins 1998
1408:
1329:
1189:
938:random walk hypothesis
906:In information science
888:Statistical randomness
879:
609:algorithmic randomness
540:
401:or steps often has no
382:
223:Continuous or discrete
176:Bernoulli distribution
35:. For other uses, see
33:Knowledge (XXG):Random
5613:Population statistics
5555:System identification
5289:Autocorrelation (ACF)
5217:Exponential smoothing
5131:Discriminant analysis
5126:Canonical correlation
4990:Partition of variance
4852:Regression validation
4696:(JonckheereâTerpstra)
4595:Likelihood-ratio test
4284:Frequentist inference
4196:Locationâscale family
4117:Sampling distribution
4082:Statistical inference
4049:Cross-sectional study
4036:Observational studies
3995:Randomized experiment
3824:Stem-and-leaf display
3626:Central limit theorem
3248:Svetlana Jitomirskaya
3155:Multiscroll attractor
3000:Interval exchange map
2953:Dyadic transformation
2938:Complex quadratic map
2780:Topological conjugacy
2715:Correlation dimension
2690:Anosov diffeomorphism
2473:Nassim Nicholas Taleb
2011:10.1101/gr.219303.116
1733:Hansen, Mogens Herman
1652:Ted.com, (May 2016).
1402:
1319:
1183:
1072:Gaming Control Boards
900:simple random samples
827:Kolmogorov randomness
704:statistical mechanics
686:Statistical mechanics
620:randomized algorithms
531:
524:History of randomness
477:computational science
374:
181:Binomial distribution
5536:Probabilistic design
5121:Principal components
4964:Exponential families
4916:Nonlinear regression
4895:General linear model
4857:Mixed effects models
4847:Errors and residuals
4824:Confounding variable
4726:Bayesian probability
4704:Van der Waerden test
4694:Ordered alternative
4459:Multiple comparisons
4338:RaoâBlackwellization
4301:Estimating equations
4257:Statistical distance
3975:Factorial experiment
3508:Arithmetic-Geometric
3258:Edward Norton Lorenz
2487:Exploring Randomness
2467:Fooled by Randomness
1272:random number tables
1261:statistically random
1039:, such as selecting
978:, which states that
915:communication theory
492:simple random sample
307:Law of large numbers
276:Marginal probability
201:Poisson distribution
50:Part of a series on
5608:Official statistics
5531:Methods engineering
5212:Seasonal adjustment
4980:Poisson regressions
4900:Bayesian regression
4839:Regression analysis
4819:Partial correlation
4791:Regression analysis
4390:Prediction interval
4385:Likelihood interval
4375:Confidence interval
4367:Interval estimation
4328:Unbiased estimators
4146:Model specification
4026:Up-and-down designs
3714:Partial correlation
3670:Index of dispersion
3588:Interquartile range
3218:Mitchell Feigenbaum
3160:Population dynamics
3145:HĂ©nonâHeiles system
3005:Irrational rotation
2958:Dynamical billiards
2943:Coupled map lattice
2803:Liouville's theorem
2735:Hausdorff dimension
2720:Conservative system
2705:Bifurcation diagram
2359:10.1038/nature09008
2351:2010Natur.464.1021P
2335:(7291): 1021â1024.
2316:ciphersbyritter.com
2123:2013CSF....55...64L
1946:2022Natur.602..101M
1847:10.1038/nature05677
1839:2007Natur.446..871G
1422:Boy or girl paradox
1300:Quantum nonlocality
1290:discrete transforms
661:Pattern recognition
599:in two dimensions.
587:wrote a chapter on
581:The Logic of Chance
536:of dice players in
507:conspiracy theories
465:Monte Carlo methods
419:information entropy
266:Complementary event
208:Probability measure
196:Pareto distribution
191:Normal distribution
5628:Spatial statistics
5508:Medical statistics
5408:First hitting time
5362:Whittle likelihood
5013:Degrees of freedom
5008:Multivariate ANOVA
4941:Heteroscedasticity
4753:Bayesian estimator
4718:Bayesian inference
4567:KolmogorovâSmirnov
4452:Randomization test
4422:Testing hypotheses
4395:Tolerance interval
4306:Maximum likelihood
4201:Exponential family
4134:Density estimation
4094:Statistical theory
4054:Natural experiment
4000:Scientific control
3917:Survey methodology
3603:Standard deviation
3396:Santa Fe Institute
3263:Aleksandr Lyapunov
3093:Three-body problem
2980:Gingerbreadman map
2867:Bifurcation theory
2745:Lyapunov stability
2417:Deborah J. Bennett
2397:The New York Times
2393:"Playing the Odds"
2250:on 20 October 2007
1668:Cristian S. Calude
1580:www.dictionary.com
1494:Probability theory
1464:Chaitin's constant
1455:Mathematics portal
1430:Monty Hall problem
1409:
1405:Monty Hall problem
1330:
1278:Measures and tests
1245:cellular automaton
1190:
1132:genetic algorithms
1128:Monte Carlo method
1025:Athenian democracy
671:Probability theory
666:Percolation theory
656:Information theory
565:Athenian democracy
541:
511:Cristian S. Calude
450:probability theory
383:
317:Boole's inequality
253:Stochastic process
142:Mutual exclusivity
59:Probability theory
5730:
5729:
5668:
5667:
5664:
5663:
5603:National accounts
5573:Actuarial science
5565:Social statistics
5458:
5457:
5454:
5453:
5450:
5449:
5385:Survival function
5370:
5369:
5232:Granger causality
5073:Contingency table
5048:Survival analysis
5025:
5024:
5021:
5020:
4877:Linear regression
4772:
4771:
4768:
4767:
4743:Credible interval
4712:
4711:
4495:
4494:
4311:Method of moments
4180:Parametric family
4141:Statistical model
4071:
4070:
4067:
4066:
3985:Random assignment
3907:Statistical power
3841:
3840:
3837:
3836:
3686:Contingency table
3656:
3655:
3523:Generalized/power
3404:
3403:
3268:BenoĂźt Mandelbrot
3233:Martin Gutzwiller
3223:Peter Grassberger
3106:
3105:
3088:Rössler attractor
2836:
2835:
2740:Invariant measure
2662:Lyapunov exponent
2523:978-0-375-42404-5
2301:978-1-349-11899-1
1940:(7895): 101â105.
1823:(7138): 871â875.
1741:. Wiley. p.
1680:Mariya I. Soskova
1414:probability space
1334:Gambler's fallacy
1317:
1090:American football
835:Andrey Kolmogorov
749:natural selection
719:quantum mechanics
676:Quantum mechanics
567:in the form of a
385:In common usage,
369:
368:
271:Joint probability
218:Bernoulli process
117:Probability space
16:(Redirected from
5760:
5718:
5717:
5706:
5705:
5695:
5694:
5680:
5679:
5583:Crime statistics
5477:
5464:
5381:
5347:Fourier analysis
5334:Frequency domain
5314:
5261:
5227:Structural break
5187:
5136:Cluster analysis
5083:Log-linear model
5056:
5031:
4972:
4946:Homoscedasticity
4802:
4778:
4697:
4689:
4681:
4680:(KruskalâWallis)
4665:
4650:
4605:Cross validation
4590:
4572:AndersonâDarling
4519:
4506:
4477:Likelihood-ratio
4469:Parametric tests
4447:Permutation test
4430:1- & 2-tails
4321:Minimum distance
4293:Point estimation
4289:
4240:Optimal decision
4191:
4090:
4077:
4059:Quasi-experiment
4009:Adaptive designs
3860:
3847:
3724:Rank correlation
3486:
3477:
3464:
3431:
3424:
3417:
3408:
3376:Butterfly effect
3288:Itamar Procaccia
3238:Brosl Hasslacher
3135:Elastic pendulum
3063:Duffing equation
3010:KaplanâYorke map
2928:Arnold's cat map
2916:
2892:Stability theory
2877:Dynamical system
2872:Control of chaos
2852:
2844:
2828:Takens's theorem
2760:Poincaré section
2630:
2612:
2605:
2598:
2589:
2515:Leonard Mlodinow
2401:
2400:
2388:
2379:
2378:
2344:
2324:
2318:
2312:
2306:
2305:
2285:
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2275:
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2255:
2240:
2234:
2228:
2222:
2221:
2219:
2195:
2189:
2188:
2149:
2143:
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2102:
2096:
2095:
2067:
2057:
2039:
2033:
2032:
2022:
1990:
1984:
1983:
1973:
1924:
1918:
1917:
1915:
1913:
1897:
1891:
1881:
1875:
1874:
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1806:
1805:
1803:
1801:
1792:
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1763:
1757:
1756:
1729:
1723:
1709:
1703:
1689:
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1609:
1603:
1597:
1591:
1590:
1588:
1586:
1572:
1563:
1554:
1538:
1527:
1499:Pseudorandomness
1484:Nonlinear system
1457:
1452:
1451:
1318:
1284:Randomness tests
1233:pseudorandomness
1108:uses a weighted
837:and his student
503:Theodore Motzkin
452:and the various
434:random sequences
361:
354:
347:
137:Elementary event
69:
47:
21:
5768:
5767:
5763:
5762:
5761:
5759:
5758:
5757:
5733:
5732:
5731:
5726:
5689:
5660:
5622:
5559:
5545:quality control
5512:
5494:Clinical trials
5471:
5446:
5430:
5418:Hazard function
5412:
5366:
5328:
5312:
5275:
5271:BreuschâGodfrey
5259:
5236:
5176:
5151:Factor analysis
5097:
5078:Graphical model
5050:
5017:
4984:
4970:
4950:
4904:
4871:
4833:
4796:
4795:
4764:
4708:
4695:
4687:
4679:
4663:
4648:
4627:Rank statistics
4621:
4600:Model selection
4588:
4546:Goodness of fit
4540:
4517:
4491:
4463:
4416:
4361:
4350:Median unbiased
4278:
4189:
4122:Order statistic
4084:
4063:
4030:
4004:
3956:
3911:
3854:
3852:Data collection
3833:
3745:
3700:
3674:
3652:
3612:
3564:
3481:Continuous data
3471:
3458:
3440:
3435:
3405:
3400:
3368:
3362:
3308:Caroline Series
3203:Mary Cartwright
3185:
3179:
3130:Double pendulum
3112:
3102:
3051:
3044:
2970:Exponential map
2921:
2907:
2901:
2859:
2853:
2846:
2832:
2798:Ergodic theorem
2791:
2784:
2775:Stable manifold
2765:Recurrence plot
2681:
2635:
2621:
2616:
2532:
2491:Gregory Chaitin
2452:Donald E. Knuth
2435:Olav Kallenberg
2409:
2407:Further reading
2404:
2390:
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2146:
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2103:
2099:
2084:
2065:10.1.1.701.3838
2041:
2040:
2036:
1999:Genome Research
1992:
1991:
1987:
1926:
1925:
1921:
1911:
1909:
1899:
1898:
1894:
1882:
1878:
1814:
1813:
1809:
1799:
1797:
1790:
1785:
1784:
1780:
1764:
1760:
1753:
1731:
1730:
1726:
1710:
1706:
1690:
1686:
1676:S. Barry Cooper
1666:
1659:
1651:
1647:
1611:
1610:
1606:
1598:
1594:
1584:
1582:
1574:
1573:
1566:
1555:
1551:
1547:
1542:
1541:
1528:
1524:
1519:
1514:
1453:
1446:
1443:
1393:
1375:
1369:
1350:
1344:
1336:
1322:audio amplifier
1310:
1308:
1286:
1280:
1201:Brownian motion
1178:
1172:
1124:quality control
1102:postseason play
1100:tied teams for
1015:
1009:
967:
951:
934:
908:
896:
890:
884:
847:Gregory Chaitin
819:random sequence
785:
760:possibilities.
737:
700:
695:
628:
557:games of chance
526:
520:
426:random variable
365:
213:Random variable
164:Bernoulli trial
43:
40:
23:
22:
15:
12:
11:
5:
5766:
5764:
5756:
5755:
5750:
5745:
5735:
5734:
5728:
5727:
5725:
5724:
5712:
5700:
5686:
5673:
5670:
5669:
5666:
5665:
5662:
5661:
5659:
5658:
5653:
5648:
5643:
5638:
5632:
5630:
5624:
5623:
5621:
5620:
5615:
5610:
5605:
5600:
5595:
5590:
5585:
5580:
5575:
5569:
5567:
5561:
5560:
5558:
5557:
5552:
5547:
5538:
5533:
5528:
5522:
5520:
5514:
5513:
5511:
5510:
5505:
5500:
5491:
5489:Bioinformatics
5485:
5483:
5473:
5472:
5467:
5460:
5459:
5456:
5455:
5452:
5451:
5448:
5447:
5445:
5444:
5438:
5436:
5432:
5431:
5429:
5428:
5422:
5420:
5414:
5413:
5411:
5410:
5405:
5400:
5395:
5389:
5387:
5378:
5372:
5371:
5368:
5367:
5365:
5364:
5359:
5354:
5349:
5344:
5338:
5336:
5330:
5329:
5327:
5326:
5321:
5316:
5308:
5303:
5298:
5297:
5296:
5294:partial (PACF)
5285:
5283:
5277:
5276:
5274:
5273:
5268:
5263:
5255:
5250:
5244:
5242:
5241:Specific tests
5238:
5237:
5235:
5234:
5229:
5224:
5219:
5214:
5209:
5204:
5199:
5193:
5191:
5184:
5178:
5177:
5175:
5174:
5173:
5172:
5171:
5170:
5155:
5154:
5153:
5143:
5141:Classification
5138:
5133:
5128:
5123:
5118:
5113:
5107:
5105:
5099:
5098:
5096:
5095:
5090:
5088:McNemar's test
5085:
5080:
5075:
5070:
5064:
5062:
5052:
5051:
5034:
5027:
5026:
5023:
5022:
5019:
5018:
5016:
5015:
5010:
5005:
5000:
4994:
4992:
4986:
4985:
4983:
4982:
4966:
4960:
4958:
4952:
4951:
4949:
4948:
4943:
4938:
4933:
4928:
4926:Semiparametric
4923:
4918:
4912:
4910:
4906:
4905:
4903:
4902:
4897:
4892:
4887:
4881:
4879:
4873:
4872:
4870:
4869:
4864:
4859:
4854:
4849:
4843:
4841:
4835:
4834:
4832:
4831:
4826:
4821:
4816:
4810:
4808:
4798:
4797:
4794:
4793:
4788:
4782:
4781:
4774:
4773:
4770:
4769:
4766:
4765:
4763:
4762:
4761:
4760:
4750:
4745:
4740:
4739:
4738:
4733:
4722:
4720:
4714:
4713:
4710:
4709:
4707:
4706:
4701:
4700:
4699:
4691:
4683:
4667:
4664:(MannâWhitney)
4659:
4658:
4657:
4644:
4643:
4642:
4631:
4629:
4623:
4622:
4620:
4619:
4618:
4617:
4612:
4607:
4597:
4592:
4589:(ShapiroâWilk)
4584:
4579:
4574:
4569:
4564:
4556:
4550:
4548:
4542:
4541:
4539:
4538:
4530:
4521:
4509:
4503:
4501:Specific tests
4497:
4496:
4493:
4492:
4490:
4489:
4484:
4479:
4473:
4471:
4465:
4464:
4462:
4461:
4456:
4455:
4454:
4444:
4443:
4442:
4432:
4426:
4424:
4418:
4417:
4415:
4414:
4413:
4412:
4407:
4397:
4392:
4387:
4382:
4377:
4371:
4369:
4363:
4362:
4360:
4359:
4354:
4353:
4352:
4347:
4346:
4345:
4340:
4325:
4324:
4323:
4318:
4313:
4308:
4297:
4295:
4286:
4280:
4279:
4277:
4276:
4271:
4266:
4265:
4264:
4254:
4249:
4248:
4247:
4237:
4236:
4235:
4230:
4225:
4215:
4210:
4205:
4204:
4203:
4198:
4193:
4177:
4176:
4175:
4170:
4165:
4155:
4154:
4153:
4148:
4138:
4137:
4136:
4126:
4125:
4124:
4114:
4109:
4104:
4098:
4096:
4086:
4085:
4080:
4073:
4072:
4069:
4068:
4065:
4064:
4062:
4061:
4056:
4051:
4046:
4040:
4038:
4032:
4031:
4029:
4028:
4023:
4018:
4012:
4010:
4006:
4005:
4003:
4002:
3997:
3992:
3987:
3982:
3977:
3972:
3966:
3964:
3958:
3957:
3955:
3954:
3952:Standard error
3949:
3944:
3939:
3938:
3937:
3932:
3921:
3919:
3913:
3912:
3910:
3909:
3904:
3899:
3894:
3889:
3884:
3882:Optimal design
3879:
3874:
3868:
3866:
3856:
3855:
3850:
3843:
3842:
3839:
3838:
3835:
3834:
3832:
3831:
3826:
3821:
3816:
3811:
3806:
3801:
3796:
3791:
3786:
3781:
3776:
3771:
3766:
3761:
3755:
3753:
3747:
3746:
3744:
3743:
3738:
3737:
3736:
3731:
3721:
3716:
3710:
3708:
3702:
3701:
3699:
3698:
3693:
3688:
3682:
3680:
3679:Summary tables
3676:
3675:
3673:
3672:
3666:
3664:
3658:
3657:
3654:
3653:
3651:
3650:
3649:
3648:
3643:
3638:
3628:
3622:
3620:
3614:
3613:
3611:
3610:
3605:
3600:
3595:
3590:
3585:
3580:
3574:
3572:
3566:
3565:
3563:
3562:
3557:
3552:
3551:
3550:
3545:
3540:
3535:
3530:
3525:
3520:
3515:
3513:Contraharmonic
3510:
3505:
3494:
3492:
3483:
3473:
3472:
3467:
3460:
3459:
3457:
3456:
3451:
3445:
3442:
3441:
3436:
3434:
3433:
3426:
3419:
3411:
3402:
3401:
3399:
3398:
3393:
3391:Predictability
3388:
3383:
3378:
3372:
3370:
3364:
3363:
3361:
3360:
3358:Lai-Sang Young
3355:
3353:James A. Yorke
3350:
3348:Amie Wilkinson
3345:
3340:
3335:
3330:
3325:
3320:
3315:
3310:
3305:
3300:
3295:
3290:
3285:
3283:Henri Poincaré
3280:
3275:
3270:
3265:
3260:
3255:
3250:
3245:
3240:
3235:
3230:
3225:
3220:
3215:
3210:
3205:
3200:
3195:
3189:
3187:
3181:
3180:
3178:
3177:
3172:
3167:
3162:
3157:
3152:
3150:Kicked rotator
3147:
3142:
3137:
3132:
3127:
3122:
3120:Chua's circuit
3116:
3114:
3108:
3107:
3104:
3103:
3101:
3100:
3095:
3090:
3085:
3080:
3075:
3070:
3065:
3060:
3054:
3052:
3049:
3046:
3045:
3043:
3042:
3040:Zaslavskii map
3037:
3035:Tinkerbell map
3032:
3027:
3022:
3017:
3012:
3007:
3002:
2997:
2992:
2987:
2982:
2977:
2972:
2967:
2966:
2965:
2955:
2950:
2945:
2940:
2935:
2930:
2924:
2922:
2919:
2913:
2903:
2902:
2900:
2899:
2894:
2889:
2884:
2882:Ergodic theory
2879:
2874:
2869:
2863:
2861:
2855:
2854:
2839:
2837:
2834:
2833:
2831:
2830:
2825:
2820:
2815:
2810:
2805:
2800:
2794:
2792:
2789:
2786:
2785:
2783:
2782:
2777:
2772:
2767:
2762:
2757:
2752:
2747:
2742:
2737:
2732:
2727:
2722:
2717:
2712:
2707:
2702:
2697:
2692:
2686:
2683:
2682:
2680:
2679:
2674:
2672:Periodic point
2669:
2664:
2659:
2654:
2649:
2644:
2638:
2636:
2633:
2627:
2623:
2622:
2617:
2615:
2614:
2607:
2600:
2592:
2586:
2585:
2576:
2567:
2562:
2557:
2551:
2545:
2539:
2531:
2530:External links
2528:
2527:
2526:
2508:
2502:
2484:
2463:
2445:
2428:
2408:
2405:
2403:
2402:
2380:
2319:
2307:
2300:
2280:
2270:
2261:
2235:
2223:
2210:(6): 602â619.
2190:
2144:
2097:
2082:
2034:
1985:
1919:
1892:
1876:
1807:
1778:
1758:
1751:
1724:
1704:
1684:
1657:
1645:
1604:
1592:
1564:
1548:
1546:
1543:
1540:
1539:
1521:
1520:
1518:
1515:
1513:
1512:
1507:
1501:
1496:
1491:
1486:
1481:
1476:
1471:
1466:
1460:
1459:
1458:
1442:
1439:
1392:
1389:
1368:
1365:
1343:
1340:
1332:Main article:
1307:
1304:
1282:Main article:
1279:
1276:
1253:
1252:
1226:
1208:
1184:The ball in a
1174:Main article:
1171:
1168:
1080:drawing straws
1011:Main article:
1008:
1005:
966:
963:
959:ancient Athens
950:
947:
933:
930:
907:
904:
886:Main article:
883:
880:
851:Per Martin-Löf
843:Ray Solomonoff
839:Per Martin-Löf
809:random numbers
784:
783:In mathematics
781:
736:
733:
708:thermodynamics
699:
696:
694:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
632:
627:
624:
522:Main article:
519:
516:
479:. By analogy,
438:random process
395:predictability
367:
366:
364:
363:
356:
349:
341:
338:
337:
336:
335:
330:
322:
321:
320:
319:
314:
312:Bayes' theorem
309:
304:
299:
294:
286:
285:
284:
283:
278:
273:
268:
260:
259:
258:
257:
256:
255:
250:
245:
243:Observed value
240:
235:
230:
228:Expected value
225:
220:
210:
205:
204:
203:
198:
193:
188:
183:
178:
168:
167:
166:
156:
155:
154:
149:
144:
139:
134:
124:
119:
111:
110:
109:
108:
103:
98:
97:
96:
86:
85:
84:
71:
70:
62:
61:
55:
54:
41:
29:Special:Random
24:
14:
13:
10:
9:
6:
4:
3:
2:
5765:
5754:
5751:
5749:
5746:
5744:
5741:
5740:
5738:
5723:
5722:
5713:
5711:
5710:
5701:
5699:
5698:
5693:
5687:
5685:
5684:
5675:
5674:
5671:
5657:
5654:
5652:
5651:Geostatistics
5649:
5647:
5644:
5642:
5639:
5637:
5634:
5633:
5631:
5629:
5625:
5619:
5618:Psychometrics
5616:
5614:
5611:
5609:
5606:
5604:
5601:
5599:
5596:
5594:
5591:
5589:
5586:
5584:
5581:
5579:
5576:
5574:
5571:
5570:
5568:
5566:
5562:
5556:
5553:
5551:
5548:
5546:
5542:
5539:
5537:
5534:
5532:
5529:
5527:
5524:
5523:
5521:
5519:
5515:
5509:
5506:
5504:
5501:
5499:
5495:
5492:
5490:
5487:
5486:
5484:
5482:
5481:Biostatistics
5478:
5474:
5470:
5465:
5461:
5443:
5442:Log-rank test
5440:
5439:
5437:
5433:
5427:
5424:
5423:
5421:
5419:
5415:
5409:
5406:
5404:
5401:
5399:
5396:
5394:
5391:
5390:
5388:
5386:
5382:
5379:
5377:
5373:
5363:
5360:
5358:
5355:
5353:
5350:
5348:
5345:
5343:
5340:
5339:
5337:
5335:
5331:
5325:
5322:
5320:
5317:
5315:
5313:(BoxâJenkins)
5309:
5307:
5304:
5302:
5299:
5295:
5292:
5291:
5290:
5287:
5286:
5284:
5282:
5278:
5272:
5269:
5267:
5266:DurbinâWatson
5264:
5262:
5256:
5254:
5251:
5249:
5248:DickeyâFuller
5246:
5245:
5243:
5239:
5233:
5230:
5228:
5225:
5223:
5222:Cointegration
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5197:Decomposition
5195:
5194:
5192:
5188:
5185:
5183:
5179:
5169:
5166:
5165:
5164:
5161:
5160:
5159:
5156:
5152:
5149:
5148:
5147:
5144:
5142:
5139:
5137:
5134:
5132:
5129:
5127:
5124:
5122:
5119:
5117:
5114:
5112:
5109:
5108:
5106:
5104:
5100:
5094:
5091:
5089:
5086:
5084:
5081:
5079:
5076:
5074:
5071:
5069:
5068:Cohen's kappa
5066:
5065:
5063:
5061:
5057:
5053:
5049:
5045:
5041:
5037:
5032:
5028:
5014:
5011:
5009:
5006:
5004:
5001:
4999:
4996:
4995:
4993:
4991:
4987:
4981:
4977:
4973:
4967:
4965:
4962:
4961:
4959:
4957:
4953:
4947:
4944:
4942:
4939:
4937:
4934:
4932:
4929:
4927:
4924:
4922:
4921:Nonparametric
4919:
4917:
4914:
4913:
4911:
4907:
4901:
4898:
4896:
4893:
4891:
4888:
4886:
4883:
4882:
4880:
4878:
4874:
4868:
4865:
4863:
4860:
4858:
4855:
4853:
4850:
4848:
4845:
4844:
4842:
4840:
4836:
4830:
4827:
4825:
4822:
4820:
4817:
4815:
4812:
4811:
4809:
4807:
4803:
4799:
4792:
4789:
4787:
4784:
4783:
4779:
4775:
4759:
4756:
4755:
4754:
4751:
4749:
4746:
4744:
4741:
4737:
4734:
4732:
4729:
4728:
4727:
4724:
4723:
4721:
4719:
4715:
4705:
4702:
4698:
4692:
4690:
4684:
4682:
4676:
4675:
4674:
4671:
4670:Nonparametric
4668:
4666:
4660:
4656:
4653:
4652:
4651:
4645:
4641:
4640:Sample median
4638:
4637:
4636:
4633:
4632:
4630:
4628:
4624:
4616:
4613:
4611:
4608:
4606:
4603:
4602:
4601:
4598:
4596:
4593:
4591:
4585:
4583:
4580:
4578:
4575:
4573:
4570:
4568:
4565:
4563:
4561:
4557:
4555:
4552:
4551:
4549:
4547:
4543:
4537:
4535:
4531:
4529:
4527:
4522:
4520:
4515:
4511:
4510:
4507:
4504:
4502:
4498:
4488:
4485:
4483:
4480:
4478:
4475:
4474:
4472:
4470:
4466:
4460:
4457:
4453:
4450:
4449:
4448:
4445:
4441:
4438:
4437:
4436:
4433:
4431:
4428:
4427:
4425:
4423:
4419:
4411:
4408:
4406:
4403:
4402:
4401:
4398:
4396:
4393:
4391:
4388:
4386:
4383:
4381:
4378:
4376:
4373:
4372:
4370:
4368:
4364:
4358:
4355:
4351:
4348:
4344:
4341:
4339:
4336:
4335:
4334:
4331:
4330:
4329:
4326:
4322:
4319:
4317:
4314:
4312:
4309:
4307:
4304:
4303:
4302:
4299:
4298:
4296:
4294:
4290:
4287:
4285:
4281:
4275:
4272:
4270:
4267:
4263:
4260:
4259:
4258:
4255:
4253:
4250:
4246:
4245:loss function
4243:
4242:
4241:
4238:
4234:
4231:
4229:
4226:
4224:
4221:
4220:
4219:
4216:
4214:
4211:
4209:
4206:
4202:
4199:
4197:
4194:
4192:
4186:
4183:
4182:
4181:
4178:
4174:
4171:
4169:
4166:
4164:
4161:
4160:
4159:
4156:
4152:
4149:
4147:
4144:
4143:
4142:
4139:
4135:
4132:
4131:
4130:
4127:
4123:
4120:
4119:
4118:
4115:
4113:
4110:
4108:
4105:
4103:
4100:
4099:
4097:
4095:
4091:
4087:
4083:
4078:
4074:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4041:
4039:
4037:
4033:
4027:
4024:
4022:
4019:
4017:
4014:
4013:
4011:
4007:
4001:
3998:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3967:
3965:
3963:
3959:
3953:
3950:
3948:
3947:Questionnaire
3945:
3943:
3940:
3936:
3933:
3931:
3928:
3927:
3926:
3923:
3922:
3920:
3918:
3914:
3908:
3905:
3903:
3900:
3898:
3895:
3893:
3890:
3888:
3885:
3883:
3880:
3878:
3875:
3873:
3870:
3869:
3867:
3865:
3861:
3857:
3853:
3848:
3844:
3830:
3827:
3825:
3822:
3820:
3817:
3815:
3812:
3810:
3807:
3805:
3802:
3800:
3797:
3795:
3792:
3790:
3787:
3785:
3782:
3780:
3777:
3775:
3774:Control chart
3772:
3770:
3767:
3765:
3762:
3760:
3757:
3756:
3754:
3752:
3748:
3742:
3739:
3735:
3732:
3730:
3727:
3726:
3725:
3722:
3720:
3717:
3715:
3712:
3711:
3709:
3707:
3703:
3697:
3694:
3692:
3689:
3687:
3684:
3683:
3681:
3677:
3671:
3668:
3667:
3665:
3663:
3659:
3647:
3644:
3642:
3639:
3637:
3634:
3633:
3632:
3629:
3627:
3624:
3623:
3621:
3619:
3615:
3609:
3606:
3604:
3601:
3599:
3596:
3594:
3591:
3589:
3586:
3584:
3581:
3579:
3576:
3575:
3573:
3571:
3567:
3561:
3558:
3556:
3553:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3524:
3521:
3519:
3516:
3514:
3511:
3509:
3506:
3504:
3501:
3500:
3499:
3496:
3495:
3493:
3491:
3487:
3484:
3482:
3478:
3474:
3470:
3465:
3461:
3455:
3452:
3450:
3447:
3446:
3443:
3439:
3432:
3427:
3425:
3420:
3418:
3413:
3412:
3409:
3397:
3394:
3392:
3389:
3387:
3386:Edge of chaos
3384:
3382:
3379:
3377:
3374:
3373:
3371:
3365:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3343:Marcelo Viana
3341:
3339:
3336:
3334:
3333:Audrey Terras
3331:
3329:
3328:Floris Takens
3326:
3324:
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3251:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3228:Celso Grebogi
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3208:Chen Guanrong
3206:
3204:
3201:
3199:
3196:
3194:
3193:Michael Berry
3191:
3190:
3188:
3182:
3176:
3173:
3171:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3117:
3115:
3109:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3069:
3068:Lorenz system
3066:
3064:
3061:
3059:
3056:
3055:
3053:
3047:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3021:
3018:
3016:
3015:Langton's ant
3013:
3011:
3008:
3006:
3003:
3001:
2998:
2996:
2993:
2991:
2990:Horseshoe map
2988:
2986:
2983:
2981:
2978:
2976:
2973:
2971:
2968:
2964:
2961:
2960:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2917:
2914:
2911:
2904:
2898:
2895:
2893:
2890:
2888:
2887:Quantum chaos
2885:
2883:
2880:
2878:
2875:
2873:
2870:
2868:
2865:
2864:
2862:
2856:
2851:
2847:
2843:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2796:
2795:
2793:
2787:
2781:
2778:
2776:
2773:
2771:
2768:
2766:
2763:
2761:
2758:
2756:
2753:
2751:
2748:
2746:
2743:
2741:
2738:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2701:
2698:
2696:
2695:Arnold tongue
2693:
2691:
2688:
2687:
2684:
2678:
2675:
2673:
2670:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2639:
2637:
2631:
2628:
2624:
2620:
2613:
2608:
2606:
2601:
2599:
2594:
2593:
2590:
2584:
2580:
2577:
2574:
2572:
2568:
2566:
2563:
2561:
2558:
2555:
2552:
2549:
2546:
2543:
2540:
2537:
2534:
2533:
2529:
2524:
2520:
2516:
2512:
2509:
2506:
2503:
2500:
2499:1-85233-417-7
2496:
2492:
2488:
2485:
2482:
2481:1-58799-190-X
2478:
2474:
2470:
2468:
2464:
2461:
2460:0-201-89684-2
2457:
2453:
2449:
2446:
2443:
2440:
2436:
2432:
2429:
2426:
2425:0-674-10745-4
2422:
2418:
2414:
2411:
2410:
2406:
2398:
2394:
2387:
2385:
2381:
2376:
2372:
2368:
2364:
2360:
2356:
2352:
2348:
2343:
2338:
2334:
2330:
2323:
2320:
2317:
2311:
2308:
2303:
2297:
2293:
2292:
2284:
2281:
2274:
2271:
2265:
2262:
2249:
2245:
2239:
2236:
2233:
2227:
2224:
2218:
2213:
2209:
2205:
2201:
2194:
2191:
2187:
2183:
2179:
2175:
2171:
2167:
2163:
2159:
2155:
2148:
2145:
2140:
2136:
2132:
2128:
2124:
2120:
2116:
2112:
2108:
2101:
2098:
2093:
2089:
2085:
2083:9781450311786
2079:
2075:
2071:
2066:
2061:
2056:
2051:
2047:
2046:
2038:
2035:
2030:
2026:
2021:
2016:
2012:
2008:
2004:
2000:
1996:
1989:
1986:
1981:
1977:
1972:
1967:
1963:
1959:
1955:
1951:
1947:
1943:
1939:
1935:
1931:
1923:
1920:
1908:
1907:
1902:
1896:
1893:
1890:
1886:
1885:Q for Quantum
1880:
1877:
1872:
1868:
1864:
1860:
1856:
1852:
1848:
1844:
1840:
1836:
1831:
1826:
1822:
1818:
1811:
1808:
1796:
1789:
1782:
1779:
1775:
1774:0-387-98844-0
1771:
1767:
1762:
1759:
1754:
1752:9780631180173
1748:
1744:
1740:
1739:
1734:
1728:
1725:
1721:
1720:0-674-01517-7
1717:
1713:
1708:
1705:
1701:
1700:0-19-512332-8
1697:
1693:
1688:
1685:
1681:
1677:
1673:
1669:
1664:
1662:
1658:
1655:
1649:
1646:
1641:
1637:
1633:
1629:
1625:
1621:
1620:
1615:
1608:
1605:
1601:
1596:
1593:
1581:
1577:
1571:
1569:
1565:
1561:
1560:
1553:
1550:
1544:
1536:
1532:
1531:almost surely
1526:
1523:
1516:
1511:
1508:
1505:
1502:
1500:
1497:
1495:
1492:
1490:
1487:
1485:
1482:
1480:
1479:Indeterminism
1477:
1475:
1472:
1470:
1467:
1465:
1462:
1461:
1456:
1450:
1445:
1440:
1438:
1435:
1431:
1425:
1423:
1417:
1415:
1406:
1401:
1397:
1390:
1388:
1386:
1385:
1379:
1374:
1373:Benford's law
1366:
1364:
1361:
1356:
1355:playing cards
1349:
1341:
1339:
1335:
1327:
1323:
1305:
1303:
1301:
1297:
1295:
1291:
1285:
1277:
1275:
1273:
1269:
1264:
1262:
1258:
1250:
1246:
1242:
1238:
1234:
1230:
1227:
1224:
1221:machines and
1220:
1216:
1212:
1209:
1206:
1202:
1198:
1195:
1194:
1193:
1187:
1182:
1177:
1169:
1167:
1165:
1161:
1157:
1153:
1149:
1145:
1143:
1139:
1135:
1133:
1129:
1125:
1121:
1120:opinion polls
1117:
1113:
1111:
1107:
1103:
1099:
1095:
1091:
1087:
1083:
1081:
1077:
1073:
1068:
1064:
1060:
1056:
1052:
1048:
1046:
1043:and military
1042:
1038:
1037:randomization
1034:
1030:
1026:
1022:
1018:
1014:
1006:
1004:
1002:
997:
995:
991:
987:
983:
981:
977:
972:
971:deterministic
964:
962:
960:
956:
948:
946:
943:
939:
931:
929:
927:
923:
918:
916:
911:
905:
903:
901:
895:
889:
882:In statistics
881:
878:
873:
871:
867:
863:
858:
856:
852:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
810:
806:
802:
798:
794:
790:
782:
780:
776:
774:
770:
766:
761:
757:
754:
750:
746:
742:
734:
732:
729:
724:
720:
715:
713:
709:
705:
697:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
633:
631:
625:
623:
621:
617:
612:
610:
606:
600:
598:
594:
590:
586:
582:
578:
572:
570:
566:
562:
558:
554:
550:
546:
539:
535:
530:
525:
517:
515:
512:
508:
504:
500:
499:Ramsey theory
497:According to
495:
493:
488:
486:
482:
478:
474:
470:
466:
462:
457:
455:
451:
447:
443:
442:deterministic
439:
435:
431:
427:
422:
420:
416:
412:
408:
404:
400:
396:
392:
388:
381:
378:
373:
362:
357:
355:
350:
348:
343:
342:
340:
339:
334:
331:
329:
326:
325:
324:
323:
318:
315:
313:
310:
308:
305:
303:
300:
298:
295:
293:
290:
289:
288:
287:
282:
279:
277:
274:
272:
269:
267:
264:
263:
262:
261:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
219:
216:
215:
214:
211:
209:
206:
202:
199:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
173:
172:
169:
165:
162:
161:
160:
157:
153:
150:
148:
145:
143:
140:
138:
135:
133:
130:
129:
128:
125:
123:
120:
118:
115:
114:
113:
112:
107:
104:
102:
101:Indeterminism
99:
95:
92:
91:
90:
87:
83:
80:
79:
78:
75:
74:
73:
72:
68:
64:
63:
60:
56:
53:
49:
48:
45:
38:
34:
30:
19:
5748:Cryptography
5719:
5707:
5688:
5681:
5593:Econometrics
5543: /
5526:Chemometrics
5503:Epidemiology
5496: /
5469:Applications
5311:ARIMA model
5258:Q-statistic
5207:Stationarity
5103:Multivariate
5046: /
5042: /
5040:Multivariate
5038: /
4978: /
4974: /
4748:Bayes factor
4647:Signed rank
4559:
4533:
4525:
4513:
4208:Completeness
4044:Cohort study
3942:Opinion poll
3877:Missing data
3864:Study design
3819:Scatter plot
3741:Scatter plot
3734:Spearman's Ï
3696:Grouped data
3338:Mary Tsingou
3303:David Ruelle
3298:Otto Rössler
3243:Michel HĂ©non
3213:Leon O. Chua
3170:Tilt-A-Whirl
3140:FPUT problem
3025:Standard map
3020:Logistic map
2845:
2619:Chaos theory
2570:
2510:
2504:
2486:
2465:
2447:
2430:
2412:
2396:
2332:
2328:
2322:
2310:
2290:
2283:
2273:
2264:
2252:. Retrieved
2248:the original
2238:
2226:
2207:
2203:
2193:
2185:
2160:(1): 19â25.
2157:
2153:
2147:
2114:
2110:
2100:
2044:
2037:
2005:(1): 66â74.
2002:
1998:
1988:
1937:
1933:
1922:
1910:. Retrieved
1904:
1895:
1889:John Gribbin
1884:
1879:
1820:
1816:
1810:
1798:. Retrieved
1794:
1781:
1765:
1761:
1737:
1727:
1711:
1707:
1691:
1687:
1648:
1623:
1617:
1607:
1595:
1583:. Retrieved
1579:
1557:
1552:
1525:
1434:booby prizes
1426:
1418:
1410:
1394:
1382:
1380:
1376:
1351:
1337:
1325:
1298:
1287:
1265:
1254:
1228:
1215:chaos theory
1210:
1196:
1191:
1147:
1146:
1137:
1136:
1115:
1114:
1085:
1084:
1050:
1049:
1020:
1019:
1016:
1007:Applications
998:
984:
968:
952:
935:
926:Alfréd Rényi
919:
912:
909:
897:
894:Random error
875:
859:
813:
786:
777:
772:
764:
762:
758:
747:followed by
738:
716:
701:
646:Cryptography
641:Chaos theory
629:
615:
613:
601:
588:
580:
573:
542:
496:
489:
458:
423:
386:
384:
333:Tree diagram
328:Venn diagram
292:Independence
238:Markov chain
122:Sample space
105:
44:
5721:WikiProject
5636:Cartography
5598:Jurimetrics
5550:Reliability
5281:Time domain
5260:(LjungâBox)
5182:Time-series
5060:Categorical
5044:Time-series
5036:Categorical
4971:(Bernoulli)
4806:Correlation
4786:Correlation
4582:JarqueâBera
4554:Chi-squared
4316:M-estimator
4269:Asymptotics
4213:Sufficiency
3980:Interaction
3892:Replication
3872:Effect size
3829:Violin plot
3809:Radar chart
3789:Forest plot
3779:Correlogram
3729:Kendall's Ï
3323:Nina Snaith
3313:Yakov Sinai
3198:Rufus Bowen
2948:Duffing map
2933:Baker's map
2858:Theoretical
2770:SRB measure
2677:Phase space
2647:Bifurcation
2581:, from the
1912:12 February
1800:20 November
1585:21 November
1535:probability
1424:for more).
1241:arithmetics
1203:, but also
1166:for more).
1164:Determinism
1116:Mathematics
1094:coin tosses
1047:lotteries.
949:In politics
855:Yongge Wang
789:probability
681:Random walk
651:Game theory
597:random walk
569:kleroterion
430:event space
415:probability
248:Random walk
89:Determinism
77:Probability
5743:Randomness
5737:Categories
5588:Demography
5306:ARMA model
5111:Regression
4688:(Friedman)
4649:(Wilcoxon)
4587:Normality
4577:Lilliefors
4524:Student's
4400:Resampling
4274:Robustness
4262:divergence
4252:Efficiency
4190:(monotone)
4185:Likelihood
4102:Population
3935:Stratified
3887:Population
3706:Dependence
3662:Count data
3593:Percentile
3570:Dispersion
3503:Arithmetic
3438:Statistics
3381:Complexity
3278:Edward Ott
3125:Convection
3050:Continuous
2725:Ergodicity
2536:QuantumLab
2413:Randomness
1906:U.C. Davis
1670:, (2017).
1545:References
1504:Random.org
1371:See also:
1346:See also:
1294:complexity
1249:seed state
1229:Randomness
1211:Randomness
1197:Randomness
1170:Generation
1156:cleromancy
1152:divination
1001:Cleromancy
980:non-random
932:In finance
922:Paul ErdĆs
892:See also:
831:compressed
805:simulation
797:Statistics
773:individual
735:In biology
691:Statistics
626:In science
616:deliberate
549:divination
461:statistics
387:randomness
159:Experiment
106:Randomness
52:statistics
4969:Logistic
4736:posterior
4662:Rank sum
4410:Jackknife
4405:Bootstrap
4223:Bootstrap
4158:Parameter
4107:Statistic
3902:Statistic
3814:Run chart
3799:Pie chart
3794:Histogram
3784:Fan chart
3759:Bar chart
3641:L-moments
3528:Geometric
3293:Mary Rees
3253:Bryna Kra
3186:theorists
2995:Ikeda map
2985:HĂ©non map
2975:Gauss map
2657:Limit set
2642:Attractor
2469:, 2nd ed.
2342:0911.3427
2117:: 64â79.
2060:CiteSeerX
2055:1201.2069
1962:1476-4687
1855:1476-4687
1830:0704.2529
1510:Sortition
1326:at random
1255:The many
1160:Free will
1033:Allotment
976:evolution
753:gene pool
745:mutations
585:John Venn
561:sortition
152:Singleton
18:By chance
5683:Category
5376:Survival
5253:Johansen
4976:Binomial
4931:Isotonic
4518:(normal)
4163:location
3970:Blocking
3925:Sampling
3804:QâQ plot
3769:Box plot
3751:Graphics
3646:Skewness
3636:Kurtosis
3608:Variance
3538:Heronian
3533:Harmonic
3369:articles
3111:Physical
3030:Tent map
2920:Discrete
2860:branches
2790:Theorems
2626:Concepts
2367:20393558
2182:72016377
2139:55589891
2092:15609415
2029:29233924
1980:35022609
1863:17443179
1735:(1991).
1722:page 370
1702:page 279
1640:37243306
1441:See also
1384:a priori
1219:pachinko
1186:roulette
1154:such as
1148:Religion
1138:Medicine
1067:roulette
1055:gambling
1029:isonomia
1021:Politics
990:Buddhist
793:gambling
769:freckles
577:calculus
553:religion
532:Ancient
233:Variance
5709:Commons
5656:Kriging
5541:Process
5498:studies
5357:Wavelet
5190:General
4357:Plug-in
4151:L space
3930:Cluster
3631:Moments
3449:Outline
3367:Related
3175:Weather
3113:systems
2906:Chaotic
2652:Fractal
2542:HotBits
2442:0854102
2375:4300790
2347:Bibcode
2254:27 July
2174:7059501
2119:Bibcode
2020:5749183
1971:8810380
1942:Bibcode
1928:2022).
1871:4412358
1835:Bibcode
1403:In the
1360:lottery
1130:and in
1110:lottery
1076:lottery
765:density
518:History
399:symbols
391:pattern
147:Outcome
5578:Census
5168:Normal
5116:Manova
4936:Robust
4686:2-way
4678:1-way
4516:-test
4187:
3764:Biplot
3555:Median
3548:Lehmer
3490:Center
3273:Hee Oh
2908:maps (
2755:Mixing
2575:Chance
2521:
2505:Random
2497:
2479:
2458:
2423:
2373:
2365:
2329:Nature
2298:
2180:
2172:
2137:
2090:
2080:
2062:
2027:
2017:
1978:
1968:
1960:
1934:Nature
1869:
1861:
1853:
1817:Nature
1772:
1749:
1718:
1698:
1638:
1104:. The
1092:, use
1086:Sports
1065:, and
1041:jurors
942:market
877:bases.
870:normal
862:log(2)
845:, and
538:Pompei
534:fresco
417:, and
380:bitmap
94:System
82:Axioms
5202:Trend
4731:prior
4673:anova
4562:-test
4536:-test
4528:-test
4435:Power
4380:Pivot
4173:shape
4168:scale
3618:Shape
3598:Range
3543:Heinz
3518:Cubic
3454:Index
3184:Chaos
2963:outer
2667:Orbit
2371:S2CID
2337:arXiv
2278:lot."
2178:S2CID
2135:S2CID
2088:S2CID
2050:arXiv
1867:S2CID
1825:arXiv
1791:(PDF)
1636:S2CID
1517:Notes
1051:Games
1045:draft
994:karma
986:Hindu
403:order
127:Event
5435:Test
4635:Sign
4487:Wald
3560:Mode
3498:Mean
2910:list
2634:Core
2554:QRNG
2548:QRBG
2519:ISBN
2495:ISBN
2477:ISBN
2456:ISBN
2421:ISBN
2363:PMID
2296:ISBN
2256:2012
2170:PMID
2078:ISBN
2025:PMID
1976:PMID
1958:ISSN
1914:2022
1859:PMID
1851:ISSN
1802:2019
1770:ISBN
1747:ISBN
1716:ISBN
1696:ISBN
1587:2019
1556:The
1223:dice
1162:and
1098:seed
1059:dice
988:and
955:tied
936:The
924:and
864:and
823:bits
739:The
723:atom
710:and
555:and
545:dice
483:use
436:. A
411:dice
4615:BIC
4610:AIC
2513:by
2489:by
2471:by
2450:by
2433:by
2415:by
2355:doi
2333:464
2212:doi
2162:doi
2158:106
2127:doi
2070:doi
2015:PMC
2007:doi
1966:PMC
1950:doi
1938:602
1843:doi
1821:446
1743:230
1628:doi
1243:or
1144:).
1082:).
913:In
767:of
471:or
393:or
5739::
2439:MR
2395:.
2383:^
2369:.
2361:.
2353:.
2345:.
2331:.
2206:.
2202:.
2184:.
2176:.
2168:.
2156:.
2133:.
2125:.
2115:55
2109:.
2086:.
2076:.
2068:.
2058:.
2023:.
2013:.
2003:28
2001:.
1997:.
1974:.
1964:.
1956:.
1948:.
1936:.
1932:.
1903:.
1887:,
1865:.
1857:.
1849:.
1841:.
1833:.
1819:.
1793:.
1745:.
1678:,
1660:^
1634:.
1624:14
1622:.
1616:.
1578:.
1567:^
1292:,
1274:.
1225:).
1207:).
1134:.
1061:,
1023::
872::
866:pi
841:,
714:.
611:.
593:pi
583:,
571:.
509:.
487:.
456:.
421:.
375:A
4560:G
4534:F
4526:t
4514:Z
4233:V
4228:U
3430:e
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3416:v
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2611:e
2604:t
2597:v
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2525:.
2501:.
2483:.
2462:.
2444:.
2427:.
2399:.
2377:.
2357::
2349::
2339::
2304:.
2258:.
2220:.
2214::
2208:9
2164::
2141:.
2129::
2121::
2094:.
2072::
2052::
2031:.
2009::
1982:.
1952::
1944::
1916:.
1873:.
1845::
1837::
1827::
1804:.
1755:.
1642:.
1630::
1589:.
360:e
353:t
346:v
39:.
20:)
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