mirror of
https://github.com/PHPOffice/PhpSpreadsheet.git
synced 2026-09-18 05:57:33 +00:00
Vincent Gao
f687d261e8
calculateInverse() treated a CDF value of exactly 0.0 as "the guess is the root" and collapsed the bracket with $b = $a, ending the search. inverse() already rejects probability <= 0, so a CDF of 0.0 inside the bisection can only be a float64 underflow at a guess far below the root - never an exact hit. It is just an ordinary "guess too low" and belongs in the existing else branch. The underflow is reached whenever a probe lands many standard deviations from the mean, so the search collapses after two or three iterations and returns whichever midpoint it was holding. BETAINV(0.5, 5000, 5000) gave 0.25, though Beta(a, a) is symmetric and its median is exactly 0.5; BETAINV(0.5, 20000, 3) gave 0.5 against a true 0.99986. Onset is around alpha = 1080 for beta = 1, where the closed form 0.5 ** (1 / alpha) is available to check against. That test also happened to stop the search for shapes where incompleteBeta declines to evaluate at all and returns 0 for every x, so inverse() now rejects alpha + beta above that documented limit up front: the CDF is identically zero there, so no quantile exists to search for. Tests cover a shape x probability grid against scipy reference values plus three checks that need no external oracle: the symmetric median, the Beta(alpha, 1) closed form, and the BETADIST round trip / mirror identity.
141 lines
2.8 KiB
PHP
141 lines
2.8 KiB
PHP
<?php
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declare(strict_types=1);
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return [
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[
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1.862243320728,
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0.52, 3, 4, 1, 3,
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],
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[
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2.164759759129,
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0.3, 7.5, 9, 1, 4,
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],
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[
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2.164759759129,
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0.3, 7.5, 9, 4, 1,
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],
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[
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7.761240188783,
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0.75, 8, 9, 5, 10,
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],
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[
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2.0,
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0.685470581055, 8, 10, 1, 3,
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],
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[
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0.303225844664,
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0.2, 4, 5, 0, 1,
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],
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[
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0.303225844664,
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0.2, 4, 5, null, null,
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],
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[
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'#VALUE!',
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'NAN', 4, 5, 0, 1,
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],
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[
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'#VALUE!',
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0.2, 'NAN', 5, 0, 1,
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],
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[
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'#VALUE!',
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0.2, 4, 'NAN', 0, 1,
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],
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[
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'#VALUE!',
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0.2, 4, 5, 'NAN', 1,
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],
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[
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'#VALUE!',
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0.2, 4, 5, 0, 'NAN',
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],
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// Large shape parameters: the CDF underflows to 0 at the low probes of the
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// bisection long before the root is reached. Onset is alpha ~ 1080 for beta = 1.
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'symmetric, median' => [
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0.5,
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0.5, 5000, 5000, 0, 1,
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],
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'symmetric, upper quartile' => [
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0.503372494704,
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0.75, 5000, 5000, 0, 1,
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],
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'symmetric, lower decile' => [
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0.493592345088,
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0.1, 5000, 5000, 0, 1,
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],
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'symmetric, median, alpha = beta = 20000' => [
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0.5,
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0.5, 20000, 20000, 0, 1,
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],
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'symmetric, scaled to [1, 3]' => [
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2.006744989408,
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0.75, 5000, 5000, 1, 3,
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],
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'beta = 1, closed form 0.5 ** (1 / alpha)' => [
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0.999861380173,
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0.5, 5000, 1, 0, 1,
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],
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'beta = 1, just above the onset' => [
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0.999370064692,
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0.5, 1100, 1, 0, 1,
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],
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'right-skewed, alpha >> beta' => [
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0.999866312606,
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0.5, 20000, 3, 0, 1,
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],
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'left-skewed, beta >> alpha' => [
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0.000133687394,
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0.5, 3, 20000, 0, 1,
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],
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'moderately large alpha' => [
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0.973403556565,
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0.25, 2000, 50, 0, 1,
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],
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'alpha so large that the quantile rounds to 1' => [
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1.0,
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0.5, 1.0e20, 3, 0, 1,
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],
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'huge symmetric shapes still give the median' => [
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0.5,
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0.5, 1.0e20, 1.0e20, 0, 1,
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],
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'alpha + beta beyond the range incompleteBeta will evaluate' => [
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'#NUM!',
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0.5, 2.0e305, 1.0e305, 0, 1,
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],
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'alpha < 0' => [
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'#NUM!',
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0.2, -4, 5, 0, 1,
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],
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'alpha = 0' => [
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'#NUM!',
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0.2, 0, 5, 0, 1,
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],
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'beta < 0' => [
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'#NUM!',
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0.2, 4, -5, 0, 1,
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],
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'beta = 0' => [
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'#NUM!',
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0.2, 4, 0, 0, 1,
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],
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'Probability < 0' => [
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'#NUM!',
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-0.5, 4, 5, 1, 3,
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],
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'Probability = 0' => [
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'#NUM!',
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0.0, 4, 5, 1, 3,
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],
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'Probability > 1' => [
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'#NUM!',
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1.5, 4, 5, 1, 3,
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],
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'Min = Max' => [
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'#NUM!',
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1, 4, 5, 1, 1,
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],
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];
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