Polyhedral Star-Shaped Distributions

<div>Pentagon <svg height="8.73791pt" id="M878" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.68809 8.94669 8.73791" width="8.94669pt" 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="M70 662V0H236V253H391C522 253 628 317 628 459C628 600 519 662 390 662H70ZM491 604C555 583 584 521 584 457C584 399 551 329 491 310V604ZM447 305C432 298 397 297 381 297H236V618H388C404 618 432 616 447 609V305ZM192 44H114V618H192V44Z" id="g197-27"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="678" vert-adv-y="678"></glyph.data></g></svg> and the convex polyhedral fan <svg height="9.48169pt" id="M879" style="vertical-align:-0.3629904pt" version="1.1" viewbox="-0.0498162 -9.1187 9.4556 9.48169" width="9.4556pt" 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="M659 678C634 653 609 641 586 641S532 659 494 695C487 690 473 677 450 658S410 624 398 613S372 588 355 571C323 536 308 504 308 473C308 425 337 376 366 344C395 313 424 265 424 218C424 179 397 159 360 159C348 159 335 163 320 170L309 148C327 138 349 133 376 133C417 133 453 147 485 174C518 201 534 233 534 268C534 374 392 449 392 525C392 548 405 572 431 598C457 567 493 552 539 552C568 552 597 567 622 595C649 624 655 634 675 662L659 678ZM624 173C558 101 487 65 410 65C323 65 256 107 219 174S164 316 164 399C164 476 184 553 231 605C255 632 283 645 315 645C341 645 362 640 379 629L395 648C372 673 340 685 300 685C116 685 47 478 47 356C47 179 152 -24 370 -24C432 -24 486 -6 533 29S617 108 644 161L624 173Z" id="g200-4"></path><glyph.data ascent="704" descent="-209" horiz-adv-x="717" vert-adv-y="717"></glyph.data></g></svg> for <svg height="8.73791pt" id="M880" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.68809 8.94669 8.73791" width="8.94669pt" 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="M70 662V0H236V253H391C522 253 628 317 628 459C628 600 519 662 390 662H70ZM491 604C555 583 584 521 584 457C584 399 551 329 491 310V604ZM447 305C432 298 397 297 381 297H236V618H388C404 618 432 616 447 609V305ZM192 44H114V618H192V44Z" id="g197-27"></path><glyph.data ascent="693" descent="-218" horiz-adv-x="678" vert-adv-y="678"></glyph.data></g></svg> in Example <a href="https://static.hindawi.com/articles/jps/volume-2017/7176897/figures/#ex1">A.1</a>.</div>

Journal of Probability and Statistics

Polyhedral Star-Shaped Distributions

Figure 12