On the Properties of the New Generalized Pareto Distribution and Its Applications

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Models</td><td class="align_center">AIC</td><td class="align_center">CAIC</td><td class="align_center">BIC</td><td class="align_center">HQIC</td><td class="align_center"><span style="width: 14.9491ptpx;"><svg height="8.78357pt" id="M152" style="vertical-align:-0.3499308pt" version="1.1" viewbox="-0.0498162 -8.43364 14.9491 8.78357" width="14.9491pt" 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="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M512 180C494 129 475 97 457 77C433 50 397 43 354 43C323 43 297 45 279 52C259 61 255 78 255 125V516C255 602 264 608 340 615V650H35V615C111 608 121 602 121 516V133C121 48 111 42 24 35V0H511C519 27 540 126 548 169L512 180Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">KEGPD <svg height="12.7961pt" id="M153" style="vertical-align:-3.23374pt" version="1.1" viewbox="-0.0498162 -9.56236 63.5468 12.7961" width="63.5468pt" 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"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M563 442L553 454L479 439C463 404 440 354 416 322H414C389 422 344 454 283 454C151 454 21 310 21 162C21 48 73 -12 135 -12C182 -12 249 19 325 126H327C339 20 368 -12 407 -12C452 -12 507 21 557 110L530 136C508 107 493 92 480 92C462 92 453 123 430 253C459 292 528 386 563 442ZM318 186C290 133 235 76 202 76C175 76 154 108 154 184C154 275 198 406 247 406C288 406 313 294 318 186Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.118,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.876,0)"><path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.384,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.142,0)"><path d="M454 656C454 669 448 679 426 679C383 679 312 658 265 630C226 635 207 659 207 675C207 690 212 708 223 725L193 730C160 721 123 692 123 655C123 623 152 590 208 583C163 553 120 514 120 447C120 404 148 372 181 358C101 318 21 252 21 160C21 81 64 41 148 16C166 11 189 5 212 0C274 -14 300 -33 300 -64C300 -103 273 -136 251 -162L282 -184C342 -139 402 -75 402 -5C402 57 356 84 287 103L238 116C183 129 141 155 141 208C141 263 181 317 225 341C261 328 294 324 325 324C353 324 398 381 398 409C398 421 392 428 369 428C335 428 296 421 270 414C240 425 223 449 223 483C223 533 256 570 272 579C317 579 385 586 396 592C421 606 454 646 454 656Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.34,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,49.483,0)"><path d="M499 509C493 596 425 703 312 703C244 703 159 654 159 573C159 542 182 485 225 430C200 416 165 396 137 376C68 327 21 268 21 176C21 77 78 -12 216 -12C269 -12 318 9 365 42C435 91 467 167 467 245S412 394 328 492C280 548 240 603 240 617S254 636 272 636C349 636 418 580 486 488L499 509ZM343 195C343 109 302 30 235 30C186 30 157 96 157 165C157 226 172 287 203 342C219 370 237 393 250 403C291 350 343 280 343 195Z"></path></g><g transform="matrix(.013,0,0,-0.013,58.882,0)"><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></td><td class="align_center">478.3736</td><td class="align_center">478.7947</td><td class="align_center">488.7943</td><td class="align_center">482.5911</td><td class="align_center">235.1868</td></tr><tr><td class="align_left">KP <svg height="12.5351pt" id="M154" style="vertical-align:-3.23372pt" version="1.1" viewbox="-0.0498162 -9.30138 52.2293 12.5351" width="52.2293pt" 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 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239 454C182 443 111 409 73 383C51 366 38 353 38 335C38 309 74 285 101 285C121 285 136 293 143 319C151 350 160 374 171 388C180 400 191 406 205 406C241 406 265 371 265 308V278C242 258 165 234 106 212C54 192 30 168 30 116C30 54 81 -12 165 -12C185 -12 232 21 270 46C274 34 281 21 295 9C308 -3 329 -12 356 -12L465 45ZM265 79C249 67 238 63 223 63C200 63 163 84 163 139C163 174 179 192 210 208C231 219 247 229 265 239V79Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.616,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.759,0)"><path d="M196 417V703C139 687 58 673 7 667V636C63 632 68 623 68 566V24C137 -2 188 -12 244 -12C390 -12 504 97 504 243C504 355 418 454 297 454C277 454 261 447 233 434L196 417ZM196 382C211 387 221 389 238 389C301 389 365 339 365 212C365 87 316 27 262 28C230 29 207 59 201 75C198 83 196 94 196 108V382Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.728,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,40.871,0)"><path d="M535 0V32C500 38 483 46 451 83C420 121 333 240 306 284C336 322 350 339 377 366C405 394 440 407 502 418V448L286 439V409C324 403 328 391 317 369C305 348 280 307 258 282C243 266 224 249 200 244V703C132 684 61 672 15 667V638C68 632 75 626 75 570V107C75 42 69 40 9 32V0H266V32C208 40 200 42 200 107V215C203 215 207 214 210 213C215 213 221 207 230 195C274 124 330 34 359 -1L535 0Z"></path></g><g transform="matrix(.013,0,0,-0.013,47.565,0)"><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></td><td class="align_center">480.2818</td><td class="align_center">480.7029</td><td class="align_center">490.7025</td><td class="align_center">484.4992</td><td class="align_center">236.6409</td></tr><tr><td class="align_left">APP <svg height="12.5351pt" id="M155" style="vertical-align:-3.23372pt" version="1.1" viewbox="-0.0498162 -9.30138 29.7985 12.5351" width="29.7985pt" 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"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M563 442L553 454L479 439C463 404 440 354 416 322H414C389 422 344 454 283 454C151 454 21 310 21 162C21 48 73 -12 135 -12C182 -12 249 19 325 126H327C339 20 368 -12 407 -12C452 -12 507 21 557 110L530 136C508 107 493 92 480 92C462 92 453 123 430 253C459 292 528 386 563 442ZM318 186C290 133 235 76 202 76C175 76 154 108 154 184C154 275 198 406 247 406C288 406 313 294 318 186Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.118,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.262,0)"><path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z"></path></g><g transform="matrix(.013,0,0,-0.013,25.156,0)"><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></td><td class="align_center">614.2206</td><td class="align_center">614.3443</td><td class="align_center">619.4309</td><td class="align_center">616.3293</td><td class="align_center">305.1103</td></tr><tr><td class="align_left">GP <svg height="12.0001pt" id="M156" style="vertical-align:-2.43774pt" version="1.1" viewbox="-0.0498162 -9.56236 27.2671 12.0001" width="27.2671pt" 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"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M454 656C454 669 448 679 426 679C383 679 312 658 265 630C226 635 207 659 207 675C207 690 212 708 223 725L193 730C160 721 123 692 123 655C123 623 152 590 208 583C163 553 120 514 120 447C120 404 148 372 181 358C101 318 21 252 21 160C21 81 64 41 148 16C166 11 189 5 212 0C274 -14 300 -33 300 -64C300 -103 273 -136 251 -162L282 -184C342 -139 402 -75 402 -5C402 57 356 84 287 103L238 116C183 129 141 155 141 208C141 263 181 317 225 341C261 328 294 324 325 324C353 324 398 381 398 409C398 421 392 428 369 428C335 428 296 421 270 414C240 425 223 449 223 483C223 533 256 570 272 579C317 579 385 586 396 592C421 606 454 646 454 656Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.696,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.839,0)"><path d="M499 509C493 596 425 703 312 703C244 703 159 654 159 573C159 542 182 485 225 430C200 416 165 396 137 376C68 327 21 268 21 176C21 77 78 -12 216 -12C269 -12 318 9 365 42C435 91 467 167 467 245S412 394 328 492C280 548 240 603 240 617S254 636 272 636C349 636 418 580 486 488L499 509ZM343 195C343 109 302 30 235 30C186 30 157 96 157 165C157 226 172 287 203 342C219 370 237 393 250 403C291 350 343 280 343 195Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.625,0)"><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></td><td class="align_center">537.4365</td><td class="align_center">537.5602</td><td class="align_center">542.6468</td><td class="align_center">539.5452</td><td class="align_center">266.7182</td></tr><tr><td class="align_left">EGP <svg height="12.0001pt" id="M157" style="vertical-align:-2.43774pt" version="1.1" viewbox="-0.0498162 -9.56236 27.2671 12.0001" width="27.2671pt" 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"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M454 656C454 669 448 679 426 679C383 679 312 658 265 630C226 635 207 659 207 675C207 690 212 708 223 725L193 730C160 721 123 692 123 655C123 623 152 590 208 583C163 553 120 514 120 447C120 404 148 372 181 358C101 318 21 252 21 160C21 81 64 41 148 16C166 11 189 5 212 0C274 -14 300 -33 300 -64C300 -103 273 -136 251 -162L282 -184C342 -139 402 -75 402 -5C402 57 356 84 287 103L238 116C183 129 141 155 141 208C141 263 181 317 225 341C261 328 294 324 325 324C353 324 398 381 398 409C398 421 392 428 369 428C335 428 296 421 270 414C240 425 223 449 223 483C223 533 256 570 272 579C317 579 385 586 396 592C421 606 454 646 454 656Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.696,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.839,0)"><path d="M499 509C493 596 425 703 312 703C244 703 159 654 159 573C159 542 182 485 225 430C200 416 165 396 137 376C68 327 21 268 21 176C21 77 78 -12 216 -12C269 -12 318 9 365 42C435 91 467 167 467 245S412 394 328 492C280 548 240 603 240 617S254 636 272 636C349 636 418 580 486 488L499 509ZM343 195C343 109 302 30 235 30C186 30 157 96 157 165C157 226 172 287 203 342C219 370 237 393 250 403C291 350 343 280 343 195Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.625,0)"><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></td><td class="align_center">527.2457</td><td class="align_center">527.3694</td><td class="align_center">532.456</td><td class="align_center">529.3544</td><td class="align_center">261.6228</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab5

Table 5

Table 5: On the Properties of the New Generalized Pareto Distribution and Its Applications 