KSLCore/ksl.utilities.distributions/Poisson

Poisson

class Poisson(theMean: Double = 1.0, name: String? = null) : Distribution, DiscretePMFInRangeDistributionIfc, LossFunctionDistributionIfc, 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

theMean

the mean rate

name

an optional label/name

Constructors

Link copied to clipboard
constructor(parameters: DoubleArray)

Constructs a Poisson using the supplied parameter

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

Types

Link copied to clipboard
object Companion

Properties

Link copied to clipboard
var mean: Double

the mean (parameter) of the poisson

Link copied to clipboard
val mode: Int
Link copied to clipboard
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

Link copied to clipboard
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
Link copied to clipboard
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)

Link copied to clipboard
open override fun instance(): Poisson
Link copied to clipboard
open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

Link copied to clipboard
open override fun mean(): Double

Returns the mean or expected value of a distribution

Link copied to clipboard
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

Link copied to clipboard
open override fun pmf(i: Int): Double

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

Link copied to clipboard
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.

Link copied to clipboard
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

Link copied to clipboard
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)

Link copied to clipboard
Link copied to clipboard
open override fun toString(): String
Link copied to clipboard
open override fun variance(): Double

Returns the variance of the distribution if defined