PHP | stats_cdf_cauchy() Function

PHP stats_cdf_cauchy() 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_cauchy() Function.

The stats_cdf_cauchy() function is used to calculate any one parameter of the cauchy distribution given values for the others.

Syntax

Following below is the syntax to use this function -

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


Parameter Details

Sr.NoParameterDescription
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 PHP function returns the cumulative distribution function, its inverse, or one of its parameters, of the cauchy distribution. The kind of the return value and 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 value of the random variable.
  • x0 denotes the location of the cauchy distribution.
  • gamma denotes the scale parameter of the cauchy distribution.

whichReturn valuepar1par2par3
1CDFxx0gamma
2xCDFx0gamma
3x0xCDFgamma
4gammaxCDFx0

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 (X, MEAN, SD).

  • P here is the cumulative cauchy distribution. Input range: [0, 1].
  • X is the value of the random variable. 
  • MEAN of the cauchy distribution.
  • SD is Standard Deviation.

<?php
   // which = 1 : calculate P from (X, MEAN, SD)
   var_dump(round(stats_cdf_cauchy(1, 2, 3, 1), 6));
?>

Output

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

float(0.397584)

Example2

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

  • P here is the cumulative cauchy distribution. Input range: [0, 1]. 
  • X is the value of the random variable.
  • MEAN of the cauchy distribution.
  • SD is Standard Deviation.

<?php
   // which = 2 : calculate X from (P, MEAN, SD)
   var_dump(round(stats_cdf_cauchy(0.397583618, 2, 3, 2), 6));
?>

Output

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

float(1)

Example3

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

  • P here is the cumulative cauchy distribution. Input range: [0, 1].
  • X is the value of the random variable.
  • MEAN of cauchy distribution.
  • SD is Standard Deviation.

<?php
   // which = 3 : calculate MEAN from (P, X, SD)
   var_dump(round(stats_cdf_cauchy(0.397583618, 1, 3, 3), 6));
?>

Output

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

float(2)

Example4

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

  • P here is the cumulative cauchy distribution. Input range: [0, 1].
  • X is the value of random variable.
  • MEAN of cauchy distribution.
  • SD is Standard Deviation.

<?php
   // which = 4 : calculate SD from (P, X, MEAN)
   var_dump(round(stats_cdf_cauchy(0.397583618, 1, 2, 4), 6));
?>

Output

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

float(0.3)

Example5

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

<?php
   var_dump(stats_cdf_cauchy(1, 2, 3, 0)); // which < 1
?>

Output

The above code will produce the following result and a warning in logs PHP Warning: stats_cdf_cauchy(): fourth parameter ought 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_cauchy(1, 2, 3, 5)); // which > 4?>
?>

Output

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

bool(false)


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_chisquare() Function in PHP.

Feel free to ask your questions where necessary and we will attend to them as soon as possible. If this tutorial was helpful to you, you can use the share button to share this tutorial.

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