MathPHP\Probability\Distribution\Continuous\Gamma Class Reference

Gamma distribution https://en.wikipedia.org/wiki/Gamma_distribution. More...

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

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

Public Member Functions
	__construct (float $k, float $θ)
	Constructor. More...
	pdf (float $x)
	Probability density function. More...
	cdf (float $x)
	Cumulative distribution function. More...
	mean ()
	Mean of the distribution. More...
	median ()
	Approximation of the median of the distribution https://en.wikipedia.org/wiki/Gamma_distribution#Median_calculation. 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
	$θ

Detailed Description

Gamma distribution https://en.wikipedia.org/wiki/Gamma_distribution.

Constructor & Destructor Documentation

__construct()

MathPHP\Probability\Distribution\Continuous\Gamma::__construct	(	float	$k,
		float	$θ
	)

Constructor.

Parameters

float	$k	shape parameter k > 0
float	$θ	scale parameter θ > 0

Member Function Documentation

cdf()

MathPHP\Probability\Distribution\Continuous\Gamma::cdf

(

float

$x

)

Cumulative distribution function.

1 / x \ cdf = --— γ | k, - | Γ(k) \ θ /

Parameters

float

$x

percentile x > 0

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

mean()

MathPHP\Probability\Distribution\Continuous\Gamma::mean

(

)

Mean of the distribution.

μ = k θ

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

median()

MathPHP\Probability\Distribution\Continuous\Gamma::median

(

)

Approximation of the median of the distribution https://en.wikipedia.org/wiki/Gamma_distribution#Median_calculation.

3k - 0.8 υ ≈ μ -----— 3k + 0.2

Returns

float

mode()

MathPHP\Probability\Distribution\Continuous\Gamma::mode

(

)

Mode of the distribution.

mode = (k - 1)θ k ≥ 1

Returns

float

pdf()

MathPHP\Probability\Distribution\Continuous\Gamma::pdf

(

float

$x

)

Probability density function.

ₓ 1 ⁻- pdf = ---— xᵏ⁻¹ e θ Γ(k)θᵏ

Parameters

float

$x

percentile x > 0

Returns

float

Implements MathPHP\Probability\Distribution\Continuous\ContinuousDistribution.

variance()

MathPHP\Probability\Distribution\Continuous\Gamma::variance

(

)

Variance of the distribution.

var[X] = kθ²

Returns

float

Member Data Documentation

PARAMETER_LIMITS

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

Initial value:

= [
        'k' => '(0,∞)'

SUPPORT_LIMITS

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

Initial value:

= [
        'x' => '(0,∞)'

---

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

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