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Distortion function

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Balbás, A.; Garrido, J.; Mayoral, S. (2008). "Properties of Distortion Risk Measures".
362: 342: 664: 554: 617: 76: 609: 536: 80: 545: 573:"Distortion Risk Measures: Coherence and Stochastic Dominance" 15: 419: 310: 496:{\displaystyle \mathbb {Q} (A)=g(\mathbb {P} (X\in A)).} 625: 36: 443: 410: 388: 365: 345: 329:{\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )} 298: 223: 184: 149: 89: 31:
may be too technical for most readers to understand
495: 426: 396: 371: 351: 328: 274: 205: 170: 131: 525:Methodology and Computing in Applied Probability 518: 516: 671:Functions related to probability distributions 645: 8: 282:. Distortion functions are used to define 652: 638: 544: 468: 467: 445: 444: 442: 418: 417: 409: 390: 389: 387: 364: 344: 319: 318: 309: 308: 297: 225: 224: 222: 183: 148: 88: 59:Learn how and when to remove this message 43:, without removing the technical details. 275:{\displaystyle {\tilde {g}}(x)=1-g(1-x)} 566: 564: 512: 41:make it understandable to non-experts 7: 606: 604: 427:{\displaystyle A\in {\mathcal {F}}} 302: 14: 608: 20: 571:Julia L. Wirch; Mary R. Hardy. 487: 484: 472: 464: 455: 449: 323: 299: 269: 257: 242: 236: 230: 194: 188: 159: 153: 126: 114: 111: 108: 96: 1: 624:. You can help Knowledge by 397:{\displaystyle \mathbb {Q} } 359:and any distortion function 692: 603: 537:10.1007/s11009-008-9089-z 284:distortion risk measures 215:dual distortion function 141:non-decreasing function 620:-related article is a 497: 428: 398: 373: 353: 330: 276: 207: 206:{\displaystyle g(1)=1} 172: 171:{\displaystyle g(0)=0} 133: 132:{\displaystyle g:\to } 498: 429: 399: 374: 354: 331: 277: 208: 173: 134: 441: 408: 386: 379:we can define a new 363: 343: 296: 221: 182: 147: 87: 381:probability measure 73:distortion function 493: 424: 404:such that for any 394: 369: 349: 326: 272: 203: 168: 129: 676:Probability stubs 633: 632: 372:{\displaystyle g} 352:{\displaystyle X} 291:probability space 233: 69: 68: 61: 683: 654: 647: 640: 612: 605: 595: 594: 592: 590: 584: 578:. Archived from 577: 568: 559: 558: 548: 520: 502: 500: 499: 494: 471: 448: 434:it follows that 433: 431: 430: 425: 423: 422: 403: 401: 400: 395: 393: 378: 376: 375: 370: 358: 356: 355: 350: 335: 333: 332: 327: 322: 314: 313: 281: 279: 278: 273: 235: 234: 226: 212: 210: 209: 204: 177: 175: 174: 169: 138: 136: 135: 130: 64: 57: 53: 50: 44: 24: 23: 16: 691: 690: 686: 685: 684: 682: 681: 680: 661: 660: 659: 658: 601: 599: 598: 588: 586: 585:on July 5, 2016 582: 575: 570: 569: 562: 522: 521: 514: 509: 439: 438: 406: 405: 384: 383: 361: 360: 341: 340: 338:random variable 336:, then for any 294: 293: 219: 218: 180: 179: 145: 144: 85: 84: 83:, for example, 65: 54: 48: 45: 37:help improve it 34: 25: 21: 12: 11: 5: 689: 687: 679: 678: 673: 663: 662: 657: 656: 649: 642: 634: 631: 630: 613: 597: 596: 560: 511: 510: 508: 505: 504: 503: 492: 489: 486: 483: 480: 477: 474: 470: 466: 463: 460: 457: 454: 451: 447: 421: 416: 413: 392: 368: 348: 325: 321: 317: 312: 307: 304: 301: 271: 268: 265: 262: 259: 256: 253: 250: 247: 244: 241: 238: 232: 229: 202: 199: 196: 193: 190: 187: 167: 164: 161: 158: 155: 152: 128: 125: 122: 119: 116: 113: 110: 107: 104: 101: 98: 95: 92: 67: 66: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 688: 677: 674: 672: 669: 668: 666: 655: 650: 648: 643: 641: 636: 635: 629: 627: 623: 619: 614: 611: 607: 602: 581: 574: 567: 565: 561: 556: 552: 547: 542: 538: 534: 530: 526: 519: 517: 513: 506: 490: 481: 478: 475: 461: 458: 452: 437: 436: 435: 414: 411: 382: 366: 346: 339: 315: 305: 292: 287: 285: 266: 263: 260: 254: 251: 248: 245: 239: 227: 216: 200: 197: 191: 185: 165: 162: 156: 150: 142: 123: 120: 117: 105: 102: 99: 93: 90: 82: 78: 74: 63: 60: 52: 49:November 2021 42: 38: 32: 29:This article 27: 18: 17: 626:expanding it 615: 600: 587:. Retrieved 580:the original 528: 524: 288: 214: 72: 70: 55: 46: 30: 618:probability 546:10016/14071 77:mathematics 665:Categories 531:(3): 385. 507:References 143:such that 81:statistics 589:March 10, 479:∈ 415:∈ 303:Ω 264:− 252:− 231:~ 112:→ 555:53327887 289:Given a 213:. The 139:, is a 35:Please 553:  616:This 583:(PDF) 576:(PDF) 551:S2CID 622:stub 591:2012 178:and 79:and 541:hdl 533:doi 217:is 75:in 39:to 667:: 563:^ 549:. 539:. 529:11 527:. 515:^ 286:. 71:A 653:e 646:t 639:v 628:. 593:. 557:. 543:: 535:: 491:. 488:) 485:) 482:A 476:X 473:( 469:P 465:( 462:g 459:= 456:) 453:A 450:( 446:Q 420:F 412:A 391:Q 367:g 347:X 324:) 320:P 316:, 311:F 306:, 300:( 270:) 267:x 261:1 258:( 255:g 249:1 246:= 243:) 240:x 237:( 228:g 201:1 198:= 195:) 192:1 189:( 186:g 166:0 163:= 160:) 157:0 154:( 151:g 127:] 124:1 121:, 118:0 115:[ 109:] 106:1 103:, 100:0 97:[ 94:: 91:g 62:) 56:( 51:) 47:( 33:.

Index

help improve it
make it understandable to non-experts
Learn how and when to remove this message
mathematics
statistics
non-decreasing function
distortion risk measures
probability space
random variable
probability measure


doi
10.1007/s11009-008-9089-z
hdl
10016/14071
S2CID
53327887


"Distortion Risk Measures: Coherence and Stochastic Dominance"
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