KSLCore/ksl.utilities.distributions/Poisson

Poisson

class Poisson(mean: Double = 1.0, name: String? = null) : Distribution, DiscretePMFInRangeDistributionIfc, LossFunctionDistributionIfc, ThirdOrderLossFunctionIfc, GetRVariableIfc, RVParametersTypeIfc(source)

Represents a Poisson random variable. A Poisson random variable represents the number of occurrences of an event with time or space.

Parameters

mean

the mean rate

name

an optional label/name

Constructors

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

Constructs a Poisson using the supplied parameter

Types

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object Companion

Properties

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var mean: Double

the mean (parameter) of the poisson

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val mode: Int
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var useRecursiveAlgorithm: Boolean

indicates whether pmf and cdf calculations are done by recursive (iterative) algorithm based on logarithms or via beta incomplete function and binomial coefficients.

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

fun cdf(x: Int): Double
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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(): Poisson
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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 mean(): Double

Returns the mean or expected value of a distribution

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open override fun parameters(): DoubleArray

Gets the parameters for the distribution

open override fun parameters(params: DoubleArray)

Sets the parameters for the distribution parameters0 should be the mean rate

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open override fun pmf(i: Int): Double

Returns the f(i) where f represents the probability mass function for the distribution.

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open override fun probIn(range: IntRange): Double

Computes the sum of the probabilities over the provided range. If the range is closed a..b then the end point b is included in the sum. If the range is open a..<b then the point b is not included in the sum.

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

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

Second-order loss function in the second factorial moment form, as in Zipkin, Foundations of Inventory Management (2000):

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open override fun thirdOrderLossFunction(x: Double): Double

G3(x) = (1/6) * Emax(X - x, 0) * max(X - x - 1, 0) * max(X - x - 2, 0), in the third factorial moment form, matching secondOrderLossFunction.

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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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