PHP - Stats CDF Laplace() Function

Definition and Usage

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

Syntax

float stats_cdf_laplace( 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

The stats_cdf_laplace() function can return the cumulative distribution function, its inverse, or one of its parameters of the Laplace distribution. The kind of return value and parameters (par1, par2, and par3) have 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.
mu denotes the location parameter of the Laplace distribution.
b denotes the scale parameter of the Laplace distribution.

which	Return value	par1	par2	par3
1	CDF	x	mu	b
2	x	CDF	mu	b
3	mu	x	CDF	b
4	b	x	CDF	mu

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 integral from 0 to X of the Laplace density. Input range: [0,1].
X is the upper limit of integration of the Laplace density. Input range: [0, +infinity).
MEAN of Laplace distribution.
SD is the Standard Deviation Laplace density.

<?php
   // which = 1 : calculate P from (X, MEAN, SD)
   var_dump(round(stats_cdf_laplace(0, 1, 2, 1), 6));
?>

Output

This will produce following result −

float(0.303265)

Example

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

P is the integral from 0 to X of the Laplace density. Input range: [0,1].
X is the upper limit of integration of the Laplace density. Input range: [0, +infinity).
MEAN of Laplace distribution.
SD is the Standard Deviation Laplace density.

<?php
   // which = 2 : calculate X from (P, MEAN, SD)
   var_dump(round(stats_cdf_laplace(0.30326533, 1, 2, 2), 6));
?>

Output

This will produce following result −

float(0)

Example

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

P is the integral from 0 to X of the Laplace density. Input range: [0,1].
X is the upper limit of integration of the Laplace density. Input range: [0, +infinity).
MEAN of Laplace distribution.
SD is the Standard Deviation Laplace density.

<?php
   // which = 3 : calculate MEAN from (P, X, SD)
   var_dump(round(stats_cdf_laplace(0.30326533, 0, 2, 3), 6));
?>

Output

This will produce following result −

float(1)

Example

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

P is the integral from 0 to X of the Laplace density. Input range: [0,1].
X is the upper limit of integration of the Laplace density. Input range: [0, +infinity).
MEAN of Laplace distribution.
SD is the Standard Deviation Laplace density.

<?php
   // which = 4 : calculate SD from (P, X, MEAN)
   var_dump(round(stats_cdf_laplace(0.30326533, 0, 1, 4), 6));
?>

Output

This will produce following result −

float(2)

Example

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

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

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_laplace(): 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_laplace(0, 1, 2, 5));      // which > 4
?>

Output

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

bool(false)