Discrete Extension of Poisson Distribution for Overdispersed Count Data: Theory and Applications

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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">Chi-square</td><td class="align_center"><svg height="10.2124pt" id="M91" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g></svg> value</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">MLE</td><td class="align_center">1.778003</td><td class="align_center">2.487436</td><td class="align_center">0.64689</td></tr><tr><td class="align_left">MPSE</td><td class="align_center">1.860611</td><td class="align_center">2.705102</td><td class="align_center">0.60832</td></tr><tr><td class="align_left">OLSE</td><td class="align_center">2.493847</td><td class="align_center">14.2504</td><td class="align_center">0.01409</td></tr><tr><td class="align_left">WLSE</td><td class="align_center">2.984391</td><td class="align_center">29.93382</td><td class="align_center">&lt;0.0001</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Different estimators with Chi-square and its <svg height="10.2124pt" id="M88" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g></svg> values for data set I.</div>

Journal of Mathematics

tab17

Table 17

Table 17: Discrete Extension of Poisson Distribution for Overdispersed Count Data: Theory and Applications 