KSLCore/ksl.utilities.distributions/Gamma

Gamma

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

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(parameters: DoubleArray)

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

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

Types

Companion

object Companion

Properties

open override val id: Int

kurtosis

val kurtosis: Double

Gets the kurtosis of the distribution

label

open override var label: String?

maxNumIterations

var maxNumIterations: Int

the maximum number of iterations for the gamma functions

val moment2: Double

val moment3: Double

val moment4: Double

open override val name: String

numericalPrecision

var numericalPrecision: Double

the numerical precision used in computing the gamma functions

parametrizedRVClass

open override val parametrizedRVClass: KClass<out ParameterizedRV>

randomVariable

open val randomVariable: RVariableIfc

rvParameters

open override val rvParameters: RVParameters

the parameters for this type of random variable

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

val skewness: Double

Gets the skewness of the distribution

Functions

cdf

open fun cdf(x: DoubleArray): DoubleArray

Returns an array of probabilities each representing F(x_i). The CDF is evaluated for each point in the input array x and the probabilities are returned in the returned array.

open fun cdf(interval: Interval): Double

Returns the probability of being in the interval, F(upper limit) - F(lower limit) Be careful, this is Pr{lower limit < = X < = upper limit} which includes the lower limit and has implications if the distribution is discrete

open fun cdf(x1: Double, x2: Double): Double

Returns the Pr{x1 <= X <= x2} for the distribution. Be careful, this is Pr{x1 <= X <= x2} which includes the lower limit and has implications if the distribution is discrete

open override fun cdf(x: Double): Double

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

complementaryCDF

open fun complementaryCDF(x: Double): Double

Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}

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

open fun invCDF(probabilities: DoubleArray): DoubleArray

Computes x_p where P(X <= x_p) = p for the supplied array of probabilities. Requires that the values within the supplied array are in (0,1)

likelihood

open fun likelihood(data: DoubleArray): Double

Assuming that the observations in the array data are from a random sample, this function computes the likelihood function. This is computed using as the sum of the log-likelihood function raised to e. Implementation may want to specify other computationally efficient formulas for this function or (most likely) the sum of the log-likelihood function.

logLikelihood

open override fun logLikelihood(x: Double): Double

Computes the natural log of the pdf function evaluated at x. Implementations may want to specify computationally efficient formulas for this function.

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

moment

fun moment(n: Int): Double

parameters

open override fun parameters(): DoubleArray

Gets the parameters for the distribution

open override fun parameters(params: DoubleArray)

Sets the parameters for the distribution with shape = parameters0 and scale = parameters1

pdf

open override fun pdf(x: Double): Double

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

randomVariable

open override fun randomVariable(stream: RNStreamIfc): RVariableIfc

open fun randomVariable(streamNum: Int): RVariableIfc

secondOrderLossFunction

open override fun secondOrderLossFunction(x: Double): Double

Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)Emax(X-x,0)*max(X-x-1,0)

standardDeviation

open fun standardDeviation(): Double

Returns the standard deviation for the distribution as the square root of the variance if it exists

sumLogLikelihood

open fun sumLogLikelihood(data: DoubleArray): Double

Computes the sum of the log-likelihood function evaluated at each observation in the data. Implementations may want to specify computationally efficient formulas for this function.

toString

open override fun toString(): String

variance

open override fun variance(): Double

Returns the variance of the distribution if defined