KSLCore/ksl.utilities.distributions/Gamma

Gamma

class Gamma(shape: Double = 1.0, scale: Double = 1.0, name: String? = null) : Distribution, ContinuousDistributionIfc, LossFunctionDistributionIfc, ThirdOrderLossFunctionIfc, InverseCDFIfc, GetRVariableIfc, RVParametersTypeIfc, MomentsIfc(source)

Models random variables that have gamma distribution For more information on the gamma distribution and its related functions, see "Object-Oriented Numerical Methods" by D. Besset

Parameters

shape

The shape parameter of the distribution, must be greater than 0

scale

The scale parameter of the distribution, must be greater than 0

name

an optional name/label

Constructors

Gamma

constructor(shape: Double = 1.0, scale: Double = 1.0, name: String? = null)

constructor(parameters: DoubleArray)

Constructs a gamma distribution with shape = parameters0 and scale = parameters1

Types

Companion

object Companion

Properties

kurtosis

open override val kurtosis: Double

Gets the kurtosis of the distribution

maxNumIterations

var maxNumIterations: Int

The maximum number of terms permitted when evaluating the incomplete gamma function for this distribution.

mean

open override val mean: Double

val moment2: Double

val moment3: Double

val moment4: Double

var numericalPrecision: Double

the numerical precision used in computing the gamma functions

scale

var scale: Double

the scale must be greater than 0.0

shape

var shape: Double

the shape must be greater than 0.0

skewness

open override val skewness: Double

Gets the skewness of the distribution

variance

open override val variance: Double

Functions

cdf

open override fun cdf(x: Double): Double

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

domain

open override fun domain(): Interval

firstOrderLossFunction

open override fun firstOrderLossFunction(x: Double): Double

Computes the first order loss function for the function for given value of x, G1(x) = Emax(X-x,0)

instance

open override fun instance(): Gamma

invCDF

open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution This is based on a numerical routine that computes the percentage points for the chi-squared distribution

logLikelihood

open override fun logLikelihood(x: Double): Double

The log-density computed directly, so a point far in the tail keeps its true value where pdf would underflow to zero: (shape - 1) ln x - x/scale - shape ln(scale) - ln Gamma(shape) for x > 0, and the ln(Double.MIN_VALUE) floor where pdf is zero.

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

moment