Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:6.36em"/><col style="width:3.89em"/><col style="width:3.74em"/><col style="width:3.82em"/></colgroup><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Search space</td><td class="align_center"><span style="width: 7.51131ptpx;"><svg height="6.1673pt" id="M90" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" 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="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 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-163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg></span></td><td class="align_center">298.29</td><td class="align_center">1.9973</td><td class="align_center">72.92</td></tr><tr><td class="align_left"><span style="width: 48.8334ptpx;"><svg height="18.7515pt" id="M94" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -15.4604 48.8334 18.7515" width="48.8334pt" 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="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path d="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.985,0)"><path d="M95 130C70 130 46 113 46 88C46 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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><g transform="matrix(.0091,0,0,-0.0091,39.233,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.18,0)"><path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"></path></g></svg></span></td><td class="align_center">302.76</td><td class="align_center">2.38</td><td class="align_center">77.35</td></tr><tr><td class="align_left"><span style="width: 48.8334ptpx;"><svg height="18.7515pt" id="M95" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -15.4604 48.8334 18.7515" width="48.8334pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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transform="matrix(.013,0,0,-0.013,22.368,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.655,-9.239)"><path d="M567 230V280H69V230H567Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.754,-9.239)"><path d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H874L901 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.695,0)"><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><g transform="matrix(.0091,0,0,-0.0091,39.233,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 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<div>Results for different search space.</div>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy 