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199:(for example), as that distribution only has one degree of freedom and changing the parameter that controls that degree (i.e. any of its central tendencies) not only shifts the distribution but reduces the height and the width of the "bump", which means that this equation doesn't hold for the Poisson distribution.
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So, if the definition of location parameter given in this article is valid, that would mean that not all central tendencies can be considered location parameters and that there is a distinction between a location parameter and a central tendency. Is there such a distinction? Where does the definition
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And although my proposed definition is informal, a formal property is implied by it. The location parameter of a point distribution is the location of the point. If a family of distributions approaches a point distribution (eg. (x-a)(1-(x-a)) as r→∞) then its location parameters must approach this
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My understanding of the notion of location and scale parameters is that they’re based on a loose concept of descriptions at varying levels of detail. You may say that data is gathered in the vicinity of m, or around m with a typical offset of s, or whatever; and a location parameter is suitably
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Well, I took the plunge and tagged the article as ‘disputed accuracy’. It’s rather absurd that an article on such an elementary topic should cause problems, but no one can fix it without having access to relevant reliable sources. Perhaps an encyclopedia of statistics is the place to look. The
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The definition shuold be expressed in terms of cumulative distribution functions. In the current form it is applicable to continuous distributions only. Moreover it seems to assume, the location parameter is the only one in the family of distributions.
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You're right. I've expanded somewhat based on your comments. However, I think it is easier to understand the concept in terms of probability densities or probability mass functions, so I've used that terminology instead of cumulative distributions.
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More generally, properties of distributions are not defined in terms of the formulae specifying them but in terms of their intrinsic behaviour.
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Consider the distribution proportional to (x-a)(1-(x-a)) in the interval and 0 outside it: would anyone say that it has
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constructed if you can’t describe the data more accurately by improving on m but only by adding detail.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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as a location parameter? The only reasonable location parameters are a+r/(r+s) and similar.
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Distinction between location parameter and central tendency?
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