A New Type 1 Alpha Power Family of Distributions and Modeling Data with Correlation, Overdispersion, and Zero-Inflation in the Health Data Sets

<div>Plots of <svg height="12.7178pt" id="M53" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 50.3372 12.7178" width="50.3372pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><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,-0.013,12.85,0)"><path d="M475 445L452 468C423 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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 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,30.21,0)"><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,-0.013,35.353,0)"><path d="M639 301C639 404 592 454 551 454C530 454 509 447 504 443L496 426C521 401 554 359 554 260C554 144 510 62 444 62C415 62 400 94 400 134C400 187 435 310 447 350L442 358L315 348C309 297 296 229 284 179C266 106 243 73 207 73C177 73 153 99 153 164C153 282 201 370 272 429L255 460C123 402 21 296 21 152C21 51 69 -12 136 -12C200 -12 253 33 291 90C300 20 331 -12 388 -12C423 -12 460 4 500 31C582 86 639 198 639 301Z"></path></g><g transform="matrix(.013,0,0,-0.013,43.965,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 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(a) Visual illustration of <svg height="12.7178pt" id="M55" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 50.3372 12.7178" width="50.3372pt" 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="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><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,-0.013,12.85,0)"><path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.325,0)"><path d="M114 412C81 412 58 388 58 355C58 321 81 297 113 297S169 321 169 355C169 388 145 412 114 412ZM95 130C70 130 46 114 46 88C46 72 54 65 59 64C93 56 121 33 121 -3C121 -41 93 -68 45 -88L56 -118C117 -99 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.468,0)"><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 405 318 306 333 204Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.854,0)"><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,-0.013,36.997,0)"><path d="M639 301C639 404 592 454 551 454C530 454 509 447 504 443L496 426C521 401 554 359 554 260C554 144 510 62 444 62C415 62 400 94 400 134C400 187 435 310 447 350L442 358L315 348C309 297 296 229 284 179C266 106 243 73 207 73C177 73 153 99 153 164C153 282 201 370 272 429L255 460C123 402 21 296 21 152C21 51 69 -12 136 -12C200 -12 253 33 291 90C300 20 331 -12 388 -12C423 -12 460 4 500 31C582 86 639 198 639 301Z"></path></g><g transform="matrix(.013,0,0,-0.013,45.609,0)"><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> for the NT1AP-W. 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Journal of Probability and Statistics

fig1

Figure 1

Figure 1: A New Type 1 Alpha Power Family of Distributions and Modeling Data with Correlation, Overdispersion, and Zero-Inflation in the Health Data Sets 

Figure 1 | A New Type 1 Alpha Power Family of Distributions and Modeling Data with Correlation, Overdispersion, and Zero-Inflation in the Health Data Sets 