Fitting the Distribution of Linear Combinations of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.4619999pt" id="M1" height="10.7762pt" version="1.1" viewBox="-0.0657574 -10.3142 16.1157 10.7762" width="16.1157pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-117" d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"/></g><g transform="matrix(.017,0,0,-0.017,5.852,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g></svg> Variables with more than 2 Degrees of Freedom

<div>Accuracy of the approximate computation of <svg height="12.6708pt" id="M162" style="vertical-align:-3.38247pt" version="1.1" viewbox="-0.0498162 -9.28833 26.8975 12.6708" width="26.8975pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.708,0)"><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,-0.013,11.206,0)"><path d="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,17.108,3.132)"><path d="M481 445L456 468C426 437 403 427 388 427C372 427 356 428 302 438C256 447 221 451 187 451C159 451 130 428 105 384C93 363 80 340 65 305L96 290C122 342 149 381 193 381C216 381 267 377 294 374S346 372 365 376L75 105C37 70 24 35 24 16C24 2 30 -5 35 -8C42 -8 46 -6 48 -2C58 14 75 35 90 41C102 46 116 46 147 32C200 8 267 -21 298 -21C347 -21 390 12 448 126L420 151C369 77 338 56 311 56C287 56 249 68 212 81C180 92 149 100 127 98C212 172 353 308 413 372L481 445Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.219,0)"><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> given in (<a href="https://static.hindawi.com/articles/jps/volume-2023/9967290/figures/#EEq27">27</a>).</div>

Journal of Probability and Statistics

fig2

Figure 2

Figure 2: Fitting the Distribution of Linear Combinations of <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.4619999pt" id="M1" height="10.7762pt" version="1.1" viewBox="-0.0657574 -10.3142 16.1157 10.7762" width="16.1157pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-117" d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"/></g><g transform="matrix(.017,0,0,-0.017,5.852,0)"><path id="g117-33" d="M535 230V280H52V230H535Z"/></g></svg> Variables with more than 2 Degrees of Freedom 

Journal of Probability and Statistics

Fitting the Distribution of Linear Combinations of Variables with more than 2 Degrees of Freedom

Figure 2