MathPHP\Probability\Distribution\Continuous\NoncentralT Class Reference

Noncentral t-distribution https://en.wikipedia.org/wiki/Noncentral_t-distribution. More...

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

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

Public Member Functions
	__construct (int $ν, float $μ)
	Constructor. More...
	pdf (float $x)
	Probability density function. More...
	cdf (float $x)
	Cumulative distribution function. More...
	mean ()
	Mean of the distribution _ /ν Γ((ν - 1)/2) E[T] = μ / - ---------— if ν > 1 √ 2 Γ(ν/2) 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
	$ν
	$μ

Detailed Description

Noncentral t-distribution https://en.wikipedia.org/wiki/Noncentral_t-distribution.

Constructor & Destructor Documentation

__construct()

MathPHP\Probability\Distribution\Continuous\NoncentralT::__construct	(	int	$ν,
		float	$μ
	)

Constructor.

Parameters

int	$ν	degrees of freedom > 0
float	$μ	Noncentrality parameter

Member Function Documentation

cdf()

MathPHP\Probability\Distribution\Continuous\NoncentralT::cdf

(

float

$x

)

Cumulative distribution function.

Fᵥ,ᵤ(x) = Fᵥ,ᵤ(x), if x ≥ 0 = 1 - Fᵥ,₋ᵤ(x) if x < 0

Parameters

float

$x

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

mean()

MathPHP\Probability\Distribution\Continuous\NoncentralT::mean

(

)

Mean of the distribution _ /ν Γ((ν - 1)/2) E[T] = μ / - ---------— if ν > 1 √ 2 Γ(ν/2)

= Does not exist if ν ≤ 1

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

pdf()

MathPHP\Probability\Distribution\Continuous\NoncentralT::pdf

(

float

$x

)

Probability density function.

/v\ / μ²\ | - | |-1*— | / ν 3 μ²x² \ / ν + 1 1 μ²x² \ \ \2/ \ 2 / / ₁F₁| - ; - ; ------— | ₁F₁| --— ; - ; ------— | | ν * Γ(ν + 1) * e | \ 2 2 2(ν + x²)/ \ 2 2 2(ν + x²)/ | ------------------------------— * | √2*μ*x * ------------------------— + -----------------------------— | ν (ν / 2) | / ν + 1 \ / ν \ | 2 * (ν + x²) * Γ(ν / 2) | (ν + x²) * Γ| ---— | √(ν + x²) * Γ| - + 1 | | \ \ 2 / \ 2 / /

Parameters

float

$x

percentile

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

Member Data Documentation

PARAMETER_LIMITS

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

Initial value:

= [
        'ν' => '(0,∞)'

SUPPORT_LIMITS

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

Initial value:

= [
        'x' => '(-∞,∞)'

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

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