PHP - Stats CDF Noncentral t() Function

Definition and Usage

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

Syntax

float stats_cdf_noncentral_t( 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_noncentral_t() function can return the cumulative distribution function, its inverse, or one of its parameters of the non-central t-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
nu denotes degrees of freedom of the distribution
mu denotes the non-centrality parameter of the distribution

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

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, PNONC).

P is the integral from 0 to X of the non-central t-density .
T is the upper limit of integration of the noncentral t-density.
DF is the degrees of freedom of the noncentral t-distribution.
PNONC is the noncentrality parameter of the noncentral t-distribution.

<?php
   // which = 1 : calculate P from (T, DF, PNONC)
   var_dump(round(stats_cdf_noncentral_t(3, 2, 1, 1), 6));
?>

Output

This will produce following result −

float(0.833559)

Example

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

P is the integral from 0 to X of the non-central t-density .
T is the upper limit of integration of the noncentral t-density.
DF is the degrees of freedom of the noncentral t-distribution.
PNONC is the noncentrality parameter of the noncentral t-distribution.

<?php
   // which = 2 : calculate T from (P, DF, PNONC)
   var_dump(round(stats_cdf_noncentral_t(0.833559426, 2, 1, 2), 6));
?>

Output

This will produce following result −

float(3)

Example

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

P is the integral from 0 to X of the non-central t-density .
T is the upper limit of integration of the noncentral t-density.
DF is the degrees of freedom of the noncentral t-distribution.
PNONC is the noncentrality parameter of the noncentral t-distribution.

<?php
   // which = 3 : calculate DF from (P, T, PNONC)
   var_dump(round(stats_cdf_noncentral_t(0.833559426, 3, 1, 3), 6));
?>

Output

This will produce following result −

float(2)

Example

In the following example when which=4, calculate PNONC from (P, DF, T).

P is the integral from 0 to X of the non-central t-density .
T is the upper limit of integration of the noncentral t-density.
DF is the degrees of freedom of the noncentral t-distribution.
PNONC is the noncentrality parameter of the noncentral t-distribution.

<?php
   // which = 4 : calculate PNONC from (P, DF, T)
   var_dump(round(stats_cdf_noncentral_t(0.833559426, 3, 2, 4), 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_noncentral_t(3, 2, 1, 0));       // which < 1
?>

Output

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

Output

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

bool(false)