Package jsl.utilities.distributions

Class Lognormal

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.Lognormal

All Implemented Interfaces:

ControllableIfc, CDFIfc, ContinuousDistributionIfc, DistributionFunctionIfc, DistributionIfc, DomainIfc, FirstOrderLossFunctionIfc, InverseCDFIfc, LossFunctionDistributionIfc, MeanIfc, PDFIfc, SecondOrderLossFunctionIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class Lognormal
extends Distribution
implements ContinuousDistributionIfc, LossFunctionDistributionIfc, InverseCDFIfc, GetRVariableIfc

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

Nested Class Summary

Nested classes/interfaces inherited from class jsl.utilities.distributions.Distribution

Distribution.RandomControls

Field Summary

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
Lognormal()	Constructs a lognormal distribution with mean 1.0 and variance 1.0
Lognormal(double[] parameters)	Constructs a lognormal distribution with mean = parameters[0] and variance = parameters[1]
Lognormal(double mean, double variance)	Constructs a lognormal distribution with mean and variance.
Lognormal(double mean, double variance, java.lang.String name)	Constructs a lognormal distribution with mean and variance.

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
double	firstOrderLossFunction(double x)	Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]
Interval	getDomain()
double	getKurtosis()	Gets the kurtosis of the distribution
double	getMean()	Returns the mean or expected value of a distribution
double	getMoment3()
double	getMoment4()
Normal	getNormal()	Provides a normal distribution with correct parameters as related to this lognormal distribution
double	getNormalMean()	The mean of the underlying normal
double	getNormalStdDev()	The standard deviation of the underlying normal
double	getNormalVariance()	The variance of the underlying normal
double[]	getParameters()	Gets the parameters for the distribution
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getSkewness()	Gets the skewness of the distribution
double	getVariance()	Returns the variance of the distribution if defined
double	invCDF(double p)	Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.
Lognormal	newInstance()	Returns a new instance
double	pdf(double x)	Returns the f(x) where f represents the probability density function for the distribution.
double	secondOrderLossFunction(double x)	Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]
void	setParameters(double[] parameters)	Sets the parameters for the distribution mean = parameters[0] and variance = parameters[1]
void	setParameters(double mean, double variance)	Sets the parameters of a lognormal distribution to mean and variance.

Methods inherited from class jsl.utilities.distributions.Distribution

getControls, getId, getName, getStandardDeviation, inverseContinuousCDFViaBisection, inverseContinuousCDFViaBisection, inverseDiscreteCDFViaSearchUp, setControls, setId, setName, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface jsl.utilities.distributions.CDFIfc

cdf, complementaryCDF

Methods inherited from interface jsl.utilities.random.rvariable.GetRVariableIfc

getRandomVariable, getRandomVariable

Methods inherited from interface jsl.utilities.distributions.VarianceIfc

getStandardDeviation

Constructor Detail

Lognormal

public Lognormal()

Constructs a lognormal distribution with mean 1.0 and variance 1.0

Lognormal

public Lognormal(double[] parameters)

Constructs a lognormal distribution with mean = parameters[0] and variance = parameters[1]

Parameters:

parameters - An array with the mean and variance

Lognormal

public Lognormal(double mean,
                 double variance)

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

Parameters:

mean - must be > 0

variance - must be > 0

Lognormal

public Lognormal(double mean,
                 double variance,
                 java.lang.String name)

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

Parameters:

mean - must be > 0

variance - must be > 0

name - an optional name/lable

Method Detail

newInstance

public final Lognormal newInstance()

Description copied from interface: NewInstanceIfc

Returns a new instance

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

the new instance

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

setParameters

public final void setParameters(double mean,
                                double variance)

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.

Parameters:

mean - must be > 0

variance - must be > 0

getMean

public final double getMean()

Description copied from interface: MeanIfc

Returns the mean or expected value of a distribution

Specified by:

getMean in interface MeanIfc

Returns:

double the mean or expected value for the distribution

getMoment3

public final double getMoment3()

Returns:

the 3rd moment

getMoment4

public final double getMoment4()

Returns:

the 4th moment

getVariance

public final double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

double the variance of the random variable

getNormal

public final Normal getNormal()

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

Returns:

The Normal distribution

getNormalMean

public final double getNormalMean()

The mean of the underlying normal

Returns:

mean of the underlying normal

getNormalVariance

public final double getNormalVariance()

The variance of the underlying normal

Returns:

variance of the underlying normal

getNormalStdDev

public final double getNormalStdDev()

The standard deviation of the underlying normal

Returns:

standard deviation of the underlying normal

cdf

public final double cdf(double x)

Description copied from interface: CDFIfc

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

Specified by:

cdf in interface CDFIfc

Parameters:

x - a double representing the upper limit

Returns:

a double representing the probability

invCDF

public final double invCDF(double p)

Description copied from interface: InverseCDFIfc

Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.

Specified by:

invCDF in interface InverseCDFIfc

Parameters:

p - The probability to be evaluated for the inverse, p must be [0,1] or an IllegalArgumentException is thrown

Returns:

The inverse cdf evaluated at the supplied probability

pdf

public final double pdf(double x)

Description copied from interface: PDFIfc

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

Specified by:

pdf in interface PDFIfc

Parameters:

x - a double representing the value to be evaluated

Returns:

f(x)

getSkewness

public final double getSkewness()

Gets the skewness of the distribution

Returns:

the skewness

getKurtosis

public final double getKurtosis()

Gets the kurtosis of the distribution

Returns:

the kurtosis

setParameters

public final void setParameters(double[] parameters)

Sets the parameters for the distribution mean = parameters[0] and variance = parameters[1]

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array of doubles representing the parameters for the distribution

getParameters

public final double[] getParameters()

Gets the parameters for the distribution

Specified by:

getParameters in interface ParametersIfc

Returns:

Returns an array of the parameters for the distribution

firstOrderLossFunction

public double firstOrderLossFunction(double x)

Description copied from interface: FirstOrderLossFunctionIfc

Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]

Specified by:

firstOrderLossFunction in interface FirstOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, E[max(X-x,0)]

secondOrderLossFunction

public double secondOrderLossFunction(double x)

Description copied from interface: SecondOrderLossFunctionIfc

Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]

Specified by:

secondOrderLossFunction in interface SecondOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, (1/2)E[max(X-x,0)*max(X-x-1,0)]

getRandomVariable

public final RVariableIfc getRandomVariable(RNStreamIfc rng)

Specified by:

getRandomVariable in interface GetRVariableIfc

Overrides:

getRandomVariable in class Distribution

Parameters:

rng - the stream to use

Returns:

a random variable