R1.2.2

KSLCore/ksl.utilities.distributions/Normal

Normal

class Normal(theMean: Double = 0.0, theVariance: Double = 1.0, name: String? = null) : Distribution, ContinuousDistributionIfc, LossFunctionDistributionIfc, InverseCDFIfc, GetRVariableIfc, RVParametersTypeIfc, MomentsIfc(source)

Models normally distributed random variables

Parameters

theMean

of the distribution

theVariance

must be > 0

name

an optional name/label

Constructors

constructor(parameters: DoubleArray)

Constructs a normal distribution with mean = parameters0 and variance = parameters1

constructor(theMean: Double = 0.0, theVariance: Double = 1.0, name: String? = null)

Types

object Companion

Properties

open override val kurtosis: Double

Gets the kurtosis of the distribution

open override var mean: Double

open override val skewness: Double

Gets the skewness of the distribution

open override var variance: Double

Functions

open override fun cdf(x: Double): Double

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

complementaryCDF

open override fun complementaryCDF(x: Double): Double

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

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)

open override fun instance(): Normal

open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

open override fun mean(): Double

Returns the mean or expected value of a distribution

open override fun parameters(): DoubleArray

Gets the parameters for the distribution

open override fun parameters(params: DoubleArray)

Sets the parameters for the distribution mean = parameters0 and variance = parameters1

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.

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

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

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)

sumLogLikelihood

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.

open override fun toString(): String

open override fun variance(): Double

Returns the variance of the distribution if defined