KSLCore/ksl.utilities.distributions/Exponential

Exponential

class Exponential(mean: Double = 1.0, name: String? = null) : Distribution, LossFunctionDistributionIfc, ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc, MomentsIfc, RVParametersTypeIfc(source)

Models exponentially distributed random variables This distribution is commonly use to model the time between events

Parameters

mean

The mean of the distribution, must be > 0.0

name

an optional label/name

Constructors

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constructor(parameters: DoubleArray)

Constructs an exponential distribution where parameter0 is the mean of the distribution

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

Properties

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open override val kurtosis: Double = 6.0
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open override var mean: Double

mean of the distribution must be > 0.0

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open override val skewness: Double = 2.0
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open override val variance: Double

Functions

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open override fun cdf(x: Double): Double

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

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open override fun domain(): Interval
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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)

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open override fun instance(): Exponential
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open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

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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.

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open override fun mean(): Double

Returns the mean or expected value of a distribution

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open override fun parameters(): DoubleArray

Gets the parameters

open override fun parameters(params: DoubleArray)

Sets the parameters

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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.

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open override fun randomVariable(streamNumber: Int, streamProvider: RNStreamProviderIfc): ExponentialRV

Promises to return a random variable that uses the supplied stream number using the supplied stream provider

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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)

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open override 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.

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open override fun toString(): String
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open override fun variance(): Double

Returns the variance of the distribution if defined