tablepress / libraries / vendor / PhpSpreadsheet / Calculation / Statistical / Distributions / Normal.php

Normal.php in TablePress – Tables in WordPress made easy 3.4, at libraries/vendor/PhpSpreadsheet/Calculation/Statistical/Distributions/Normal.php

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1	<?php
2
3	namespace TablePress\PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
4
5	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
6	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Engineering;
7	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Exception;
8	use TablePress\PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
9
10	class Normal
11	{
12	use ArrayEnabled;
13
14	public const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
15
16	/**
17	* NORMDIST.
18	*
19	* Returns the normal distribution for the specified mean and standard deviation. This
20	* function has a very wide range of applications in statistics, including hypothesis
21	* testing.
22	*
23	* @param mixed $value Float value for which we want the probability
24	* Or can be an array of values
25	* @param mixed $mean Mean value as a float
26	* Or can be an array of values
27	* @param mixed $stdDev Standard Deviation as a float
28	* Or can be an array of values
29	* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
30	* Or can be an array of values
31	*
32	* @return array<mixed>\|float\|string The result, or a string containing an error
33	* If an array of numbers is passed as an argument, then the returned result will also be an array
34	* with the same dimensions
35	*/
36	public static function distribution($value, $mean, $stdDev, $cumulative)
37	{
38	if (is_array($value) \|\| is_array($mean) \|\| is_array($stdDev) \|\| is_array($cumulative)) {
39	return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $mean, $stdDev, $cumulative);
40	}
41
42	try {
43	$value = DistributionValidations::validateFloat($value);
44	$mean = DistributionValidations::validateFloat($mean);
45	$stdDev = DistributionValidations::validateFloat($stdDev);
46	$cumulative = DistributionValidations::validateBool($cumulative);
47	} catch (Exception $e) {
48	return $e->getMessage();
49	}
50
51	if ($stdDev < 0) {
52	return ExcelError::NAN();
53	}
54
55	if ($cumulative) {
56	return 0.5 * (1 + Engineering\Erf::erfValue(($value - $mean) / ($stdDev * sqrt(2))));
57	}
58
59	return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (($value - $mean) ** 2 / (2 * ($stdDev * $stdDev))));
60	}
61
62	/**
63	* NORMINV.
64	*
65	* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
66	*
67	* @param mixed $probability Float probability for which we want the value
68	* Or can be an array of values
69	* @param mixed $mean Mean Value as a float
70	* Or can be an array of values
71	* @param mixed $stdDev Standard Deviation as a float
72	* Or can be an array of values
73	*
74	* @return array<mixed>\|float\|string The result, or a string containing an error
75	* If an array of numbers is passed as an argument, then the returned result will also be an array
76	* with the same dimensions
77	*/
78	public static function inverse($probability, $mean, $stdDev)
79	{
80	if (is_array($probability) \|\| is_array($mean) \|\| is_array($stdDev)) {
81	return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $mean, $stdDev);
82	}
83
84	try {
85	$probability = DistributionValidations::validateProbability($probability);
86	$mean = DistributionValidations::validateFloat($mean);
87	$stdDev = DistributionValidations::validateFloat($stdDev);
88	} catch (Exception $e) {
89	return $e->getMessage();
90	}
91
92	if ($stdDev < 0) {
93	return ExcelError::NAN();
94	}
95
96	return (self::inverseNcdf($probability) * $stdDev) + $mean;
97	}
98
99	/*
100	* inverse_ncdf.php
101	* -------------------
102	* begin : Friday, January 16, 2004
103	* copyright : (C) 2004 Michael Nickerson
104	* email : [email protected]
105	*
106	*/
107	private static function inverseNcdf(float $p): float
108	{
109	// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
110	// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
111	// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
112	// I have not checked the accuracy of this implementation. Be aware that PHP
113	// will truncate the coeficcients to 14 digits.
114
115	// You have permission to use and distribute this function freely for
116	// whatever purpose you want, but please show common courtesy and give credit
117	// where credit is due.
118
119	// Input parameter is $p - probability - where 0 < p < 1.
120
121	// Coefficients in rational approximations
122	/** @var array<int, float> */
123	static $a = [
124	1 => -3.969683028665376e+01,
125	2 => 2.209460984245205e+02,
126	3 => -2.759285104469687e+02,
127	4 => 1.383577518672690e+02,
128	5 => -3.066479806614716e+01,
129	6 => 2.506628277459239e+00,
130	];
131
132	/** @var array<int, float> */
133	static $b = [
134	1 => -5.447609879822406e+01,
135	2 => 1.615858368580409e+02,
136	3 => -1.556989798598866e+02,
137	4 => 6.680131188771972e+01,
138	5 => -1.328068155288572e+01,
139	];
140
141	/** @var array<int, float> */
142	static $c = [
143	1 => -7.784894002430293e-03,
144	2 => -3.223964580411365e-01,
145	3 => -2.400758277161838e+00,
146	4 => -2.549732539343734e+00,
147	5 => 4.374664141464968e+00,
148	6 => 2.938163982698783e+00,
149	];
150
151	/** @var array<int, float> */
152	static $d = [
153	1 => 7.784695709041462e-03,
154	2 => 3.224671290700398e-01,
155	3 => 2.445134137142996e+00,
156	4 => 3.754408661907416e+00,
157	];
158
159	// Define lower and upper region break-points.
160	$p_low = 0.02425; //Use lower region approx. below this
161	$p_high = 1 - $p_low; //Use upper region approx. above this
162
163	if (0 < $p && $p < $p_low) {
164	// Rational approximation for lower region.
165	$q = sqrt(-2 * log($p));
166
167	return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6])
168	/ (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
169	} elseif ($p_high < $p && $p < 1) {
170	// Rational approximation for upper region.
171	$q = sqrt(-2 * log(1 - $p));
172
173	return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6])
174	/ (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
175	}
176
177	// Rational approximation for central region.
178	$q = $p - 0.5;
179	$r = $q * $q;
180
181	return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q
182	/ ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
183	}
184	}
185