A Mixture of Generalized Tukey’s <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.5268pt" id="M1" height="12.3952pt" version="1.1" viewBox="-0.0657574 -7.8684 9.93214 12.3952" width="9.93214pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-104" d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z"/></g></svg> Distributions

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Distribution of three parameters </td><td class="align_center" colspan="3">Parameters</td><td class="align_center" colspan="2">Test of adjusted</td></tr><tr class="thead"><td class="align_center"><span style="width: 7.30254ptpx;"><svg height="9.49473pt" id="M241" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.30254 9.49473" width="7.30254pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 7.52435ptpx;"><svg height="9.39034pt" id="M242" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.52435 9.39034" width="7.52435pt" 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="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="569" vert-adv-y="569"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 6.59789ptpx;"><svg height="9.49473pt" id="M243" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><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" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g></svg></span></td><td class="align_center">AD <svg height="11.5564pt" id="M244" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 18.9942 11.5564" width="18.9942pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z" id="g121-35"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="756" vert-adv-y="756"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.326,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td><td class="align_center">KS <svg height="11.5564pt" id="M245" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 18.9942 11.5564" width="18.9942pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M594 629L561 652L159 -9L190 -32L594 629ZM194 635C92 635 49 534 49 453C49 374 92 272 193 272C295 272 338 374 338 454S295 635 194 635ZM193 605C257 605 265 504 265 453C265 405 257 302 194 302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z" id="g121-35"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="756" vert-adv-y="756"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,14.326,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left"> Lognormal </td><td class="align_center">5.7407</td><td class="align_center">0.5265</td><td class="align_center">798.2540</td><td class="align_center">37.53</td><td class="align_center">12.3041</td></tr><tr><td class="align_left">Log-Logistic </td><td class="align_center">3.0225</td><td class="align_center">283.8185</td><td class="align_center">824.1814</td><td class="align_center">32.68</td><td class="align_center">11.1367</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Estimates for adjusting the LS<svg height="11.5564pt" id="M240" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 18.2504 11.5564" width="18.2504pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M682 0V35C628 42 606 55 571 149C504 321 444 490 381 665L329 651C264 480 191 303 129 145C94 57 78 42 17 35V0H239V35C166 47 162 58 179 111C219 237 260 350 307 481H311C353 362 406 215 445 105C461 59 458 44 395 35V0H682Z" id="g5-140"></path><glyph.data ascent="3481" descent="-2878" horiz-adv-x="699" vert-adv-y="699"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,13.619,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g></svg>.

Journal of Probability and Statistics

tab3

Table 3

Table 3: A Mixture of Generalized Tukey’s <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.5268pt" id="M1" height="12.3952pt" version="1.1" viewBox="-0.0657574 -7.8684 9.93214 12.3952" width="9.93214pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-104" d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z"/></g></svg> Distributions 

Journal of Probability and Statistics

A Mixture of Generalized Tukey’s Distributions

Table 3