PHP - Stats CDF Beta() Function

Definition and Usage

The stats_cdf_beta() function can calculate any one parameter of beta distribution given values for the others.

Syntax

float stats_cdf_beta( float $par1, float $par2, float $par3, int $which)

Parameters

Sr.No	Parameter	Description
1	par1	The first parameter
2	par2	The second parameter
3	par3	The third parameter
4	which	The flag to determine what to be calculated

Return Values

This function returns CDF(cumulativeDistribution Function), x( its inverse,),or one of its parameters, of the beta distribution(alpha, or beta). The kind of the return value and parameters (par1, par2, and par3) are determined by which.

Return value and parameters

The following table lists the return value and parameters by which.

CDF denotes cumulative distribution function.
x denotes the value of the random variable.
alpha, and beta denotes shape parameters of the beta distribution.

which	Return value	par1	par2	par3
1	CDF	x	alpha	beta
2	x	CDF	alpha	beta
3	alpha	x	CDF	beta
4	beta	x	CDF	alpha

Dependencies

This function was first introduced in statistics extension (PHP 4.0.0 and PEAR 1.4.0). We have used latest release of stats-2.0.3 (PHP 7.0.0 or newer and PEAR 1.4.0 or newer) for this tutorial.

Example

In the following example when which=1, calculate P from (X, A, B).

P is the integral from 0 to X of the chi-square distribution. Input range: [0, 1] .
X is upper limit of integration of beta density. Input range: [0,1].
A is the first parameter of the beta density. Input range: (0, +infinity).
B is the second parameter of the beta density. Input range: (0, +infinity).

<?php
   // which = 1 : calculate P from (X, A, B)
   var_dump(round(stats_cdf_beta(0.5, 2, 4, 1), 6));
?>

Output

This will produce following result −

float(0.8125)

Example

In the following example when which=2, calculate X from (P, A, B).

P is the integral from 0 to X of the chi-square distribution. Input range: [0, 1] .
X is upper limit of integration of beta density. Input range: [0,1].
A is the first parameter of the beta density. Input range: (0, +infinity).
B is the second parameter of the beta density. Input range: (0, +infinity).

<?php
   // which = 2 : calculate X from (P, A, B)
   var_dump(round(stats_cdf_beta(0.8125, 2, 4, 2), 6));
?>

Output

This will produce following result −

float(0.5)

Example

In the following example when which=3, calculate A from (P, X, B).

P is the integral from 0 to X of the chi-square distribution. Input range: [0, 1] .
X is upper limit of integration of beta density. Input range: [0,1].
A is the first parameter of the beta density. Input range: (0, +infinity).
B is the second parameter of the beta density. Input range: (0, +infinity).

<?php
   // which = 3 : calculate A from (P, X, B)
   var_dump(round(stats_cdf_beta(0.8125, 0.5, 4, 3), 6));
?>

Output

This will produce following result −

float(2)

Example

In the following example when which=4, calculate B from (P, X, A).

P is the integral from 0 to X of the chi-square distribution. Input range: [0, 1] .
X is upper limit of integration of beta density. Input range: [0,1].
A is the first parameter of the beta density. Input range: (0, +infinity).
B is the second parameter of the beta density. Input range: (0, +infinity).

<?php
   // which = 4 : calculate B from (P, X, A)
   var_dump(round(stats_cdf_beta(0.8125, 0.5, 2, 4), 6));
?>

Output

This will produce following result −

float(4)

Example

Following is an error case. In the following example which<1, warning is displayed in logs.

<?php
   var_dump(stats_cdf_beta(0.5, 2, 4, 0));     // which < 1
?>

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_beta(): Fourth parameter should be in the 1..4 range

bool(false)

Example

Following is an error case. In the following example which>4, warning is displayed in logs.

<?php
   var_dump(stats_cdf_beta(0.5, 2, 4, 5));     // which > 4
?>

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_beta(): Fourth parameter should be in the 1..4 range

bool(false)