The New Odd Log-Logistic Generalized Inverse Gaussian Regression Model

<div>Index plot for <span class="nowrap"><svg height="9.49471pt" id="M387" style="vertical-align:-0.1933298pt" version="1.1" viewbox="-0.0498162 -9.30138 6.79362 9.49471" width="6.79362pt" 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="M492 495C492 605 449 703 334 703C135 703 21 416 21 218C21 107 47 -12 184 -12C394 -12 492 307 492 495ZM367 550C367 493 360 437 353 395H170C197 528 252 661 315 661C364 661 367 588 367 550ZM344 339C323 195 267 30 198 30C160 30 147 91 147 162C147 223 150 293 159 339H344Z"></path></g></svg>:</span> (a) <svg height="12.5925pt" id="M388" style="vertical-align:-3.29112pt" version="1.1" viewbox="-0.0498162 -9.30138 36.0251 12.5925" width="36.0251pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.185,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.078,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.134,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.632,0)"><path d="M492 495C492 605 449 703 334 703C135 703 21 416 21 218C21 107 47 -12 184 -12C394 -12 492 307 492 495ZM367 550C367 493 360 437 353 395H170C197 528 252 661 315 661C364 661 367 588 367 550ZM344 339C323 195 267 30 198 30C160 30 147 91 147 162C147 223 150 293 159 339H344Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.326,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> (likelihood distance) and (b) <svg height="12.5925pt" id="M389" style="vertical-align:-3.29112pt" version="1.1" viewbox="-0.0498162 -9.30138 37.343 12.5925" width="37.343pt" 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="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.501,0)"><path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.394,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.45,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.948,0)"><path d="M492 495C492 605 449 703 334 703C135 703 21 416 21 218C21 107 47 -12 184 -12C394 -12 492 307 492 495ZM367 550C367 493 360 437 353 395H170C197 528 252 661 315 661C364 661 367 588 367 550ZM344 339C323 195 267 30 198 30C160 30 147 91 147 162C147 223 150 293 159 339H344Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.641,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> (generalized Cook’s distance).</div>

Journal of Probability and Statistics

fig8

Figure 8

Figure 8: The New Odd Log-Logistic Generalized Inverse Gaussian Regression Model 