On Properties of Length-Biased Exponential Model

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Method</td><td class="align_center"><span style="width: 6.59789ptpx;"><svg height="12.783pt" id="M164" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.5766 6.59789 12.783" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,1.031,-3.549)"><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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z"></path></g></svg></span></td><td class="align_center"><span style="width: 7.68094ptpx;"><svg height="16.0061pt" id="M165" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -12.5766 7.68094 16.0061" width="7.68094pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,2.355,-3.549)"><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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g></svg></span></td><td class="align_center">KS</td><td class="align_center">PV</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">MLE</td><td class="align_center">1.845</td><td class="align_center">0.83</td><td class="align_center">0.089</td><td class="align_center">0.619</td></tr><tr><td class="align_left">CVME</td><td class="align_center">2.207</td><td class="align_center">0.744</td><td class="align_center">0.069</td><td class="align_center">0.883</td></tr><tr><td class="align_left">ADE</td><td class="align_center">2.086</td><td class="align_center">0.773</td><td class="align_center">0.073</td><td class="align_center">0.838</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The goodness-of-fit statistics for parameters estimated under various methods for the first dataset.</div>

Mathematical Problems in Engineering

On Properties of Length-Biased Exponential Model

Table 9