MathPHP\Probability\Distribution\Continuous\ChiSquared Class Reference

χ²-distribution (Chi-squared) https://en.wikipedia.org/wiki/Chi-squared_distribution. More...

Inheritance diagram for MathPHP\Probability\Distribution\Continuous\ChiSquared:

Collaboration diagram for MathPHP\Probability\Distribution\Continuous\ChiSquared:

Public Member Functions
	__construct (float $k)
	Constructor. More...
	pdf (float $x)
	Probability density function. More...
	cdf (float $x)
	Cumulative distribution function. More...
	mean ()
	Mean of the distribution. More...
	median ()
	Median - closed form approximation. More...
	mode ()
	Mode of the distribution. More...
	variance ()
	Variance of the distribution. More...
Public Member Functions inherited from MathPHP\Probability\Distribution\Continuous\Continuous
	inverse (float $target)
	The Inverse CDF of the distribution. More...
	between (float $x₁, float $x₂)
	CDF between - probability of being between two points, x₁ and x₂ The area under a continuous distribution, that lies between two specified points. More...
	outside (float $x₁, float $x₂)
	CDF outside - Probability of being below x₁ and above x₂. More...
	above (float $x)
	CDF above - Probability of being above x to ∞ Area under a continuous distribution, that lies above a specified point. More...
	rand ()
	Produce a random number with a particular distribution. More...
Public Member Functions inherited from MathPHP\Probability\Distribution\Distribution
	__construct (... $params)
	Constructor. More...

Public Attributes
const	PARAMETER_LIMITS
const	SUPPORT_LIMITS
Public Attributes inherited from MathPHP\Probability\Distribution\Continuous\Continuous
const	GUESS_THRESHOLD = 10
const	GUESS_ALLOWANCE = 8

Protected Attributes
	$k

Detailed Description

χ²-distribution (Chi-squared) https://en.wikipedia.org/wiki/Chi-squared_distribution.

Constructor & Destructor Documentation

__construct()

MathPHP\Probability\Distribution\Continuous\ChiSquared::__construct

(

float

$k

)

Constructor.

Parameters

float

$k

degrees of freedom parameter k >= 1

Member Function Documentation

cdf()

MathPHP\Probability\Distribution\Continuous\ChiSquared::cdf

(

float

$x

)

Cumulative distribution function.

Cumulative t value up to a point, left tail.

     / k   x  \
  γ |  - , -  |
     \ 2   2 /

CDF = ----------— / k \ Γ | - | \ 2 /

Parameters

float

$x

Chi-square critical value (CV) > 0

Returns

float cumulative probability

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

mean()

MathPHP\Probability\Distribution\Continuous\ChiSquared::mean

(

)

Mean of the distribution.

μ = k

Returns

float k

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

median()

MathPHP\Probability\Distribution\Continuous\ChiSquared::median

(

)

Median - closed form approximation.

/ 2 \³ median ≈ k | 1 - - | \ k /

Returns

float

mode()

MathPHP\Probability\Distribution\Continuous\ChiSquared::mode

(

)

Mode of the distribution.

max(k - 2, 0)

Returns

float

pdf()

MathPHP\Probability\Distribution\Continuous\ChiSquared::pdf

(

float

$x

)

Probability density function.

1 -----------— x⁽ᵏ/²⁾⁻¹ ℯ⁻⁽ˣ/²⁾ χ²(k) = / k \ 2ᵏ/² Γ | - | \ 2 /

Parameters

float

$x

point at which to evaluate > 0

Returns

float probability

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

variance()

MathPHP\Probability\Distribution\Continuous\ChiSquared::variance

(

)

Variance of the distribution.

var[X] = 2k

Returns

float

Member Data Documentation

PARAMETER_LIMITS

const MathPHP\Probability\Distribution\Continuous\ChiSquared::PARAMETER_LIMITS

Initial value:

= [
        'k' => '[1,∞)'

SUPPORT_LIMITS

const MathPHP\Probability\Distribution\Continuous\ChiSquared::SUPPORT_LIMITS

Initial value:

= [
        'x' => '[0,∞)'

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The documentation for this class was generated from the following file:

• src/Probability/Distribution/Continuous/ChiSquared.php