KSLCore/ksl.utilities.distributions/Lognormal

Lognormal

class Lognormal(mean: Double = 1.0, variance: Double = 1.0, name: String? = null) : Distribution, ContinuousDistributionIfc, LossFunctionDistributionIfc, ThirdOrderLossFunctionIfc, 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

mean

must be > 0

variance

must be > 0

name

an optional name/label

Constructors

Lognormal

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

constructor(parameters: DoubleArray)

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

Properties

kurtosis

open override val kurtosis: Double

Gets the kurtosis of the distribution

mean

open override var mean: Double

moment3

val moment3: Double

moment4

val moment4: Double

normalMean

var normalMean: Double

The mean of the underlying normal

normalStdDev

var normalStdDev: Double

The standard deviation of the underlying normal

normalVariance

val normalVariance: Double

The variance of the underlying normal

skewness

open override val skewness: Double

Gets the skewness of the distribution

variance

open override var variance: Double

Functions

cdf

open override fun cdf(x: Double): Double

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

domain

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)

instance

open override fun instance(): Lognormal

invCDF

open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

logLikelihood

open override fun logLikelihood(x: Double): Double

The log-density computed directly, so a point far in the tail keeps its true value where pdf would underflow to zero: -ln x - ln(sigma) - ln(2 pi)/2 - z^2/2 with z = (ln x - mu)/sigma for x > 0, and the ln(Double.MIN_VALUE) floor where pdf is zero.

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

normal

fun normal(): Normal

Provides a normal distribution with correct parameters as related to this lognormal distribution

parameters

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(mean: Double, variance: 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.

pdf

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.

randomVariable

open override fun randomVariable(streamNumber: Int = 0, streamProvider: RNStreamProviderIfc = KSLRandom.DefaultRNStreamProvider): LognormalRV

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

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

thirdOrderLossFunction

open override fun thirdOrderLossFunction(x: Double): Double

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

toString

open override fun toString(): String

variance

open override fun variance(): Double

Returns the variance of the distribution if defined