PHP - Stats CDF F() Function

Definition and Usage

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

Syntax

float stats_cdf_f ( 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 can return cumulative distribution function, its inverse, or one of its parameters of the F 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.
d1 denotes the degree of freedoms of the F distribution.
d2 denotes the degree of freedoms of the F distribution.

which	Return value	par1	par2	par3
1	CDF	x	d1	d2
2	x	CDF	d1	d2
3	d1	x	CDF	d2
4	d2	x	CDF	d1

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 (F, DFN, DFD).

P is the integral from 0 to F of the f-density. Input range: [0,1].
F is the upper limit of integration of the f-density. Input range: [0, +infinity).
DFN is the degrees of freedom of the numerator sum of squares.
DFD is the degrees of freedom of the denominator sum of squares.

<?php
   // which = 1 : calculate P from (F, DFN, DFD)
   var_dump(round(stats_cdf_f(1, 3, 2, 1), 6));
?>

Output

This will produce following result −

float(0.464758)

Example

In the following example when which=2, calculate F from (P, DFN, DFD).

P is the integral from 0 to F of the f-density. Input range: [0,1].
F is the upper limit of integration of the f-density. Input range: [0, +infinity).
DFN is the degrees of freedom of the numerator sum of squares.
DFD is the degrees of freedom of the denominator sum of squares.

<?php
   // which = 2 : calculate F from (P, DFN, DFD)
   var_dump(round(stats_cdf_f(0.464758002, 3, 2, 2), 6));
?>

Output

This will produce following result −

float(1)

Example

In the following example when which=3, calculate DFN from (P, F, DFD).

P is the integral from 0 to F of the f-density. Input range: [0,1].
F is the upper limit of integration of the f-density. Input range: [0, +infinity).
DFN is the degrees of freedom of the numerator sum of squares.
DFD is the degrees of freedom of the denominator sum of squares.

<?php
   // which = 3 : calculate DFN from (P, F, DFD)
   var_dump(round(stats_cdf_f(0.464758002, 1, 2, 3), 6));
?>

Output

This will produce following result −

float(3)

Example

In the following example when which=4, calculate DFD from (P, F, DFN).

P is the integral from 0 to F of the f-density. Input range: [0,1].
F is the upper limit of integration of the f-density. Input range: [0, +infinity).
DFN is the degrees of freedom of the numerator sum of squares.
DFD is the degrees of freedom of the denominator sum of squares.

<?php
   // which = 4 : calculate DFD from (P, F, DFN)
   var_dump(round(stats_cdf_f(0.464758002, 1, 3, 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_f(1, 3, 2, 0)); // which < 1
?>

Output

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

Output

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

bool(false)