PHP | stats_cdf_negative_binomial() Function

Hello folks! welcome back to a new edition of our tutorial on PHP. In this tutorial guide, we are going to be studying about the PHP stats_cdf_negative_binomial() Function.

The stats_cdf_negative_binomial() function in PHP calculates any one parameter of the negative binomial distribution given values for the others.

Syntax

Following below is the syntax to use this function -

float stats_cdf_negative_binomial ( float $par1, float $par2, float $par3, int $which )

READ: PHP | stats_cdf_logistic() Function

Parameter Details

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 Value

This built-in PHP function returns the CDF, its inverse, or one of its parameters of the negative binomial distribution. The kind of the return value and the parameters (par1, par2 and par3) are determined by which.

The following table list the return value and parameters by which.

• CDF denotes cumulative distribution function.

• x denotes the number of failures.

• r denotes the number of success.

• p denotes the success rate for each trial.

which	Return value	par1	par2	par3
1	CDF	x	r	p
2	x	CDF	r	p
3	r	x	CDF	p
4	p	x	CDF	r

Dependencies

This built-in function was first introduced in statistics extension (PHP version 4.0.0 and PEAR v1.4.0). In this tutorial guide, we used the latest release of stats-2.0.3 (PHP v7.0.0 or newer and PEAR version 1.4.0 or newer).

Example1

In the following example below, when which = 1, calculate P from (S, XN, PR).

• P is the cumulative from 0 to S of the negative binomial distribution. Input range: [0, 1].

• S is the upper limit of cumulation of the negative binomial distribution. There are F or fewer failures before the XN success.

• XN is the number of successes.

• PR is the probability of success in each of the binomial trial.

<?php
   // which = 1 : calculate P from (S, XN, PR)
   var_dump(round(stats_cdf_negative_binomial(2, 1, 0.4, 1), 6));
?>

Output

When the above code is executed, it will produce the following result -

float(0.784)

Example2

In the following example below, when which = 2, calculate S from (P, XN, PR).

• P is the cumulative from 0 to S of the negative binomial distribution. Input range: [0, 1].

• S is the upper limit of cumulation of the negative binomial distribution. There are F or fewer failures before the XN success.

• XN is the number of successes.

• PR is the probability of success in each of the binomial trial.

<?php
   // which = 2 : calculate S from (P, XN, PR)
   var_dump(round(stats_cdf_negative_binomial(0.784, 1, 0.4, 2), 6));
?>

Output

When the above code is executed, it will produce the following result -

float(2)

Example3

In the following example below, when which = 3, calculate XN from (P, S, PR).

• P is the cumulative from 0 to S of the negative binomial distribution. Input range: [0, 1].

• S is the upper limit of cumulation of the negative binomial distribution. There are F or fewer failures before the XN success.

• XN is the number of successes.

• PR is the probability of success in each of the binomial trial.

<?php
   // which = 3 : calculate XN from (P, S, PR)
   var_dump(round(stats_cdf_negative_binomial(0.784, 2, 0.4, 3), 6));
?>

Output

When the above code is executed, it will produce the following result -

float(1)

Example4

In the following example below, when which = 4, calculate PR from (P, S, XN).

• P is the cumulative from 0 to S of the negative binomial distribution. Input range: [0, 1].

• S is the upper limit of cumulation of the negative binomial distribution. There are F or fewer failures before the XN success.

• XN is the number of successes.

• PR is the probability of success in each of the binomial trial.

<?php
   // which = 4 : calculate PR from (P, S, XN)
   var_dump(round(stats_cdf_negative_binomial(0.784, 2, 1, 4), 6));
?>

Output

When the above code is executed, it will produce the following result -

float(0.4)

Example5

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

<?php
   var_dump(stats_cdf_negative_binomial(2, 1, 0.4, 0));    // which < 1
?>

Output

The above code will produce the following result and a warning in logs PHP Warning: stats_cdf_negative_binomial(): The fourth parameter should to be in the 1..4 range.

bool(false)

Example6

Following is an error case. In the following example below which>4, warning message is displayed in logs.

<?php
   var_dump(stats_cdf_negative_binomial(2, 1, 0.4, 5));    // which > 4
?>

Output

The above code will produce the following result and a warning in logs PHP Warning: stats_cdf_negative_binomial(): The fourth parameter should to be in the 1..4 range.

bool(false)

READ: PHP | stats_cdf_beta() Function

Alright guys! This is where we are going to be rounding up for this tutorial post. In our next tutorial, we are going to be discussing about the stats_cdf_noncentral_chisquare() Function in PHP.

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Thanks for reading and bye for now.