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PHP - Stats CDF Cauchy() Function

Definition and Usage

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

Syntax

float stats_cdf_cauchy ( 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

Returns the cumulative distribution function, its inverse, or one of its parameters, of the Cauchy distribution. 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.

  • x0 denotes the location of the Cauchy distribution.

  • gamma denotes the scale parameter of the Cauchy distribution.

which Return value par1 par2 par3
1 CDF x x0 gamma
2 x CDF x0 gamma
3 x0 x CDF gamma
4 gamma x CDF x0

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, MEAN, SD).

  • P is the cumulation cauchy distribution. Input range: [0, 1] .

  • X is the value of the random variable.

  • MEAN of cauchy distribution.

  • SD is Standard Deviation.

<?php
   // which = 1 : calculate P from (X, MEAN, SD)
   var_dump(round(stats_cdf_cauchy(1, 2, 3, 1), 6));
?>

Output

This will produce following result −

float(0.397584)

Example

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

  • P is the cumulation cauchy distribution. Input range: [0, 1] .

  • X is the value of the random variable.

  • MEAN of cauchy distribution.

  • SD is Standard Deviation.

<?php
   // which = 2 : calculate X from (P, MEAN, SD)
   var_dump(round(stats_cdf_cauchy(0.397583618, 2, 3, 2), 6));
?>

Output

This will produce following result −

float(1)

Example

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

  • P is the cumulation cauchy distribution. Input range: [0, 1] .

  • X is the value of the random variable.

  • MEAN of cauchy distribution.

  • SD is Standard Deviation.

<?php
   // which = 3 : calculate MEAN from (P, X, SD)
   var_dump(round(stats_cdf_cauchy(0.397583618, 1, 3, 3), 6));
?>

Output

This will produce following result −

float(2)

Example

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

  • P is the cumulation cauchy distribution. Input range: [0, 1] .

  • X is the value of the random variable.

  • MEAN of cauchy distribution.

  • SD is Standard Deviatio.

<?php
   // which = 4 : calculate SD from (P, X, MEAN)
   var_dump(round(stats_cdf_cauchy(0.397583618, 1, 2, 4), 6));
?>

Output

This will produce following result −

float(0.3)

Example

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

<?php
   var_dump(stats_cdf_cauchy(1, 2, 3, 0)); // which < 1
?>

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_cauchy(): 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_cauchy(1, 2, 3, 5)); // which > 4?>
?>

Output

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

bool(false)
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