KSLCore/ksl.utilities.distributions/Lognormal

Lognormal

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

Models the lognormal distribution This distribution is commonly used to model the time of a task

Parameters: mean and variance.

Note: these parameters are the actual mean and variance of the lognormal distribution, not some underlying normal distribution as in many implementations.

Parameters

theMean

must be > 0

theVariance

must be > 0

name

an optional name/label

Constructors

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constructor(parameters: DoubleArray)

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

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

Properties

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open override val kurtosis: Double

Gets the kurtosis of the distribution

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open override var mean: Double
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var normalMean: Double

The mean of the underlying normal

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var normalStdDev: Double

The standard deviation of the underlying normal

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val normalVariance: Double

The variance of the underlying normal

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open override val skewness: Double

Gets the skewness of the distribution

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open override var 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(): Lognormal
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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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fun normal(): Normal

Provides a normal distribution with correct parameters as related to this lognormal 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 mean = parameters0 and variance = parameters1

fun parameters(theMean: Double, theVariance: Double)

Sets the parameters of a lognormal distribution to mean and variance. Note: these parameters are the actual mean and variance of the lognormal, not the underlying normal as in many other implementations.

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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): LognormalRV

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

Returns the variance of the distribution if defined