KSLCore/ksl.utilities.distributions/Exponential

Exponential

class Exponential(mean: Double = 1.0, name: String? = null) : Distribution, LossFunctionDistributionIfc, ThirdOrderLossFunctionIfc, 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(mean: Double = 1.0, name: String? = null)
constructor(parameters: DoubleArray)

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

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

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

The natural log of pdf at x: -ln(mean) - x/mean on the support, and the ln(Double.MIN_VALUE) floor used by PDFIfc outside it. The support test is the one pdf uses, so a value within numerical tolerance of zero counts as zero rather than as negative.

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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 = 0, streamProvider: RNStreamProviderIfc = KSLRandom.DefaultRNStreamProvider): 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

The second order loss function, (1/2)Emax(X-x,0)^2.

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open override fun sumLogLikelihood(data: DoubleArray): Double

The sum of logLikelihood over data, using the closed form for the observations on the support and the floor for each one outside it, so the two methods agree for every input.

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open override fun thirdOrderLossFunction(x: Double): Double

The third order loss function, (1/6)Emax(X-x,0)^3.

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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

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