Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Variable</td><td class="align_center" colspan="2">Estimator (s.e)</td></tr><tr class="thead"><td class="align_center"><span style="width: 5.60619ptpx;"><svg height="9.4556pt" id="M145" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 5.60619 9.4556" width="5.60619pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.144,-.222)"><path d="M470 557C393 591 314 624 246 666H224C156 624 76 591 0 557L12 532C86 550 163 573 235 596C309 572 384 550 458 532L470 557Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z"></path></g></svg></span></td><td class="align_center"><span style="width: 10.3951ptpx;"><svg height="9.4556pt" id="M146" style="vertical-align:-0.2063894pt" version="1.1" viewbox="-0.0498162 -9.24921 10.3951 9.4556" width="10.3951pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.572,-.222)"><path d="M658 557C549 593 437 629 340 673H318C222 629 109 593 0 557L9 532C116 551 225 577 329 602C435 576 543 551 649 532L658 557Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Reported claims</td><td class="align_center">0.6538 (0.0710)</td><td class="align_center">477.0055 (53.2312)</td></tr><tr><td class="align_left">Settled claims</td><td class="align_center">0.8596 (0.0978)</td><td class="align_center">74.7975 (7.3175)</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Parameter estimates from the negative binomial.</div>

Journal of Probability and Statistics

tab9

Table 9

Table 9: Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims 