PHP - Stats CDF t() Function

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Definition and Usage

The stats_cdf_t() function can calculate any one parameter of t-distribution given values for the others.

Syntax

float stats_cdf_t( float $par1, float $par2, int $which )

Parameters

Return Values

The stats_cdf_t() function can return the cumulative distribution function, its inverse, or one of its parameters of the t-distribution. The kind of return value and parameters (par1 and par2) 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.

• nu denotes the degrees of freedom of the t-distribution.

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 (T, DF).

• P is the integral from -infinity to t of the t-density. Input range: [0,1].

• T is the upper limit of integration of the t-density.

• DF is the degrees of freedom of the t-distribution.

<?php
   // which = 1 : calculate P from (T, DF)
   var_dump(round(stats_cdf_t(1, 1, 1), 6));
?>

Output

This will produce following result −

float(0.75)

Example

In the following example when which=2, calculate T from (P, DF).

• P is the integral from -infinity to t of the t-density. Input range: [0,1].

• T is the upper limit of integration of the t-density.

• DF is the degrees of freedom of the t-distribution.

<?php
   // which = 2 : calculate T from (P, DF)
   var_dump(round(stats_cdf_t(0.75, 1, 2), 6));
?>

Output

This will produce following result −

float(1)

Example

In the following example when which=3, calculate DF from (P, T).

• P is the integral from -infinity to t of the t-density. Input range: [0,1].

• T is the upper limit of integration of the t-density.

• DF is the degrees of freedom of the t-distribution.

<?php
   // which = 3 : calculate DF from (P, T)
   var_dump(round(stats_cdf_t(0.75, 1, 3), 6));
?>

Output

This will produce following result −

float(1)

Example

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

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

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_t(): Third parameter should be in the 1..3 range

bool(false)

Example

Following is an error case. In the following example which>3, warning is displayed in logs.

<?php
   var_dump(stats_cdf_t(1, 1, 4));      // which > 3
?>

Output

This will produce following result and a warning in logs PHP Warning: stats_cdf_t(): Third parameter should be in the 1..3 range

bool(false)