Knowledge (XXG)

Abe Sklar

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can be expressed in terms of copulas. This representation of distribution functions, which is valid in any dimension and unique when the margins are continuous, is the basis of
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Menger, Karl; Schweizer, Berthold; Sklar, Abe; Sigmund; Schmetterer, Leopold; Gruber, Peter M.; Hlawka, Edmund, eds. (2002).
430: 236:, a widespread data analytical technique used in statistics; this representation is often termed Sklar's representation. 681: 676: 593: 225: 217: 166: 161:(November 25, 1925 – October 30, 2020) was an American mathematician and a professor of applied mathematics at the 237: 190: 194: 81: 482: 631: 626: 233: 486: 380: 308: 240:
are also named after Sklar and Berthold Schweizer, who studied them together in the early 1960s.
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Karl Menger - Reminiscences of the Vienna Circle and the Mathematical Colloquium
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Sklar, A. (1959), "Fonctions de répartition à n dimensions et leurs marges",
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Menger, Karl; Schweizer, Berthold; Sklar, Abe; Sigmund, Karl, eds. (2003).
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in 1942, when he was only 16. Sklar went on to become a student of
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Summation Formulas Associated with a Class of Dirichlet Series
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Golland, Louise; McGuinness, Brian; Sklar, Abe, eds. (1994).
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to Jewish parents who immigrated to the United States from
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In 1959, Sklar introduced the notion of and the name of "
581: 489:(2016) Principles of Copula Theory, CRC Press, pp. ix 138: 126: 108: 98: 77: 54: 28: 21: 417:, IIT College of Science, retrieved 2019-05-03. 501:"Copulae: An overview and recent developments" 230:multivariate cumulative distribution functions 601: 8: 224:and proved the theorem that bears his name, 647:American people of Ukrainian-Jewish descent 608: 594: 385:: CS1 maint: location missing publisher ( 313:: CS1 maint: location missing publisher ( 18: 652:California Institute of Technology alumni 516: 459: 256:. Dordrecht: Kluwer Academic Publishers. 657:Illinois Institute of Technology faculty 351:Schweizer, Berthold; Sklar, Abe (2005). 400: 499:Größer, Joshua; Okhrin, Ostap (2022). 378: 306: 7: 642:21st-century American mathematicians 637:20th-century American mathematicians 562: 560: 165:(Illinois Tech) and the inventor of 328:. Wien; New York: Springer-Verlag. 580:. You can help Knowledge (XXG) by 203:California Institute of Technology 86:California Institute of Technology 16:American mathematician (1925–2020) 14: 564: 542:Publ. Inst. Statist. Univ. Paris 442:Genest, Christian (2021-01-01). 163:Illinois Institute of Technology 103:Illinois Institute of Technology 667:American probability theorists 505:WIREs Computational Statistics 1: 431:Mathematics Genealogy Project 325:Selecta mathematica. Volume 2 282:Selecta Mathematica. Volume 1 662:University of Chicago alumni 354:Probabilistic metric spaces 698: 559: 193:and later enrolled at the 152: 91: 444:"A tribute to Abe Sklar" 672:American mathematicians 238:Schweizer–Sklar t-norms 191:Von Steuben High School 461:10.1515/demo-2021-0110 572:This article about a 195:University of Chicago 82:University of Chicago 177:Education and career 682:Mathematician stubs 677:People from Chicago 448:Dependence Modeling 413:2019-05-02 at the 222:probability theory 181:Sklar was born in 171:probability theory 589: 588: 518:10.1002/wics.1557 364:978-0-486-14375-0 335:978-3-211-83834-1 292:978-3-7091-6110-4 228:. That is, that 211:Marjorie Senechal 156: 155: 147:Marjorie Senechal 139:Doctoral students 93:Scientific career 39:November 25, 1925 689: 610: 603: 596: 568: 561: 551: 549: 537: 531: 530: 520: 496: 490: 483:Fabrizio Durante 480: 474: 473: 463: 439: 433: 424: 418: 405: 390: 384: 376: 357:. Mineola, N.Y. 347: 318: 312: 304: 275: 207:Clark Kimberling 143:Clark Kimberling 128:Doctoral advisor 122: 61: 58:October 30, 2020 38: 36: 19: 697: 696: 692: 691: 690: 688: 687: 686: 617: 616: 615: 614: 557: 555: 554: 539: 538: 534: 498: 497: 493: 481: 477: 441: 440: 436: 425: 421: 415:Wayback Machine 406: 402: 397: 377: 365: 350: 336: 321: 305: 293: 278: 264: 249: 246: 234:copula modeling 226:Sklar's theorem 179: 145: 120: 84: 73: 63: 59: 50: 40: 34: 32: 24: 17: 12: 11: 5: 695: 693: 685: 684: 679: 674: 669: 664: 659: 654: 649: 644: 639: 634: 629: 619: 618: 613: 612: 605: 598: 590: 587: 586: 569: 553: 552: 532: 491: 475: 454:(1): 200–224. 434: 419: 399: 398: 396: 393: 392: 391: 363: 348: 334: 319: 291: 276: 262: 245: 242: 199:Tom M. Apostol 189:. He attended 178: 175: 154: 153: 150: 149: 140: 136: 135: 133:Tom M. Apostol 130: 124: 123: 112: 106: 105: 100: 96: 95: 89: 88: 79: 75: 74: 64: 62:(aged 94) 56: 52: 51: 41: 30: 26: 25: 22: 15: 13: 10: 9: 6: 4: 3: 2: 694: 683: 680: 678: 675: 673: 670: 668: 665: 663: 660: 658: 655: 653: 650: 648: 645: 643: 640: 638: 635: 633: 630: 628: 625: 624: 622: 611: 606: 604: 599: 597: 592: 591: 585: 583: 579: 575: 574:mathematician 570: 567: 563: 558: 547: 544:(in French), 543: 536: 533: 528: 524: 519: 514: 510: 506: 502: 495: 492: 488: 484: 479: 476: 471: 467: 462: 457: 453: 449: 445: 438: 435: 432: 428: 423: 420: 416: 412: 409: 404: 401: 394: 388: 382: 374: 370: 366: 360: 356: 355: 349: 345: 341: 337: 331: 327: 326: 320: 316: 310: 302: 298: 294: 288: 284: 283: 277: 273: 269: 265: 263:0-7923-2711-X 259: 255: 254: 248: 247: 243: 241: 239: 235: 231: 227: 223: 219: 214: 212: 208: 204: 200: 196: 192: 188: 184: 176: 174: 172: 168: 164: 160: 151: 148: 144: 141: 137: 134: 131: 129: 125: 118: 117: 113: 111: 107: 104: 101: 97: 94: 90: 87: 83: 80: 76: 71: 67: 57: 53: 48: 44: 31: 27: 20: 582:expanding it 571: 556: 545: 541: 535: 508: 504: 494: 478: 451: 447: 437: 422: 403: 353: 324: 281: 252: 244:Bibliography 215: 180: 158: 157: 114: 99:Institutions 92: 60:(2020-10-30) 632:2020 deaths 627:1925 births 487:Carlo Sempi 621:Categories 395:References 301:1149922502 285:. Vienna. 35:1925-11-25 548:: 229–231 527:1939-5108 470:2300-2298 427:Abe Sklar 408:Abe Sklar 381:cite book 373:873840651 344:492462474 309:cite book 159:Abe Sklar 78:Education 23:Abe Sklar 411:Archived 272:30026523 70:Illinois 47:Illinois 429:at the 220:" into 218:copulas 201:at the 187:Ukraine 183:Chicago 167:copulas 66:Chicago 43:Chicago 525:  468:  371:  361:  342:  332:  299:  289:  270:  260:  121:(1956) 119:  110:Thesis 576:is a 511:(3). 72:, USA 49:, USA 578:stub 523:ISSN 485:and 466:ISSN 387:link 369:OCLC 359:ISBN 340:OCLC 330:ISBN 315:link 297:OCLC 287:ISBN 268:OCLC 258:ISBN 209:and 55:Died 29:Born 513:doi 456:doi 169:in 623:: 521:. 509:14 507:. 503:. 464:. 450:. 446:. 383:}} 379:{{ 367:. 338:. 311:}} 307:{{ 295:. 266:. 213:. 173:. 68:, 45:, 609:e 602:t 595:v 584:. 550:. 546:8 529:. 515:: 472:. 458:: 452:9 389:) 375:. 346:. 317:) 303:. 274:. 37:) 33:(

Index

Chicago
Illinois
Chicago
Illinois
University of Chicago
California Institute of Technology
Illinois Institute of Technology
Thesis
Summation Formulas Associated with a Class of Dirichlet Series
Doctoral advisor
Tom M. Apostol
Clark Kimberling
Marjorie Senechal
Illinois Institute of Technology
copulas
probability theory
Chicago
Ukraine
Von Steuben High School
University of Chicago
Tom M. Apostol
California Institute of Technology
Clark Kimberling
Marjorie Senechal
copulas
probability theory
Sklar's theorem
multivariate cumulative distribution functions
copula modeling
Schweizer–Sklar t-norms

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