umontreal.iro.lecuyer.probdist

Class FatigueLifeDist

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.FatigueLifeDist

All Implemented Interfaces:

Distribution

public class FatigueLifeDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the fatigue life distribution with location parameter μ, scale parameter β and shape parameter γ. Its density is

f (x) = [(((x - μ)/β)^1/2 + (β/(x - μ))^1/2)/(2γ(x - μ))]φ((((x - μ)/β)^1/2 - (β/(x - μ))^1/2)/γ), for x > μ,

where φ is the probability density of the standard normal distribution. The distribution function is given by

F(x) = Φ((((x - μ)/β)^1/2 - (β/(x - μ))^1/2)/γ), for x > μ,

where Φ is the standard normal distribution function. Restrictions: β > 0, γ > 0.

The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

Constructors

Constructor and Description
FatigueLifeDist(double mu, double beta, double gamma) Constructs a fatigue life distribution with parameters μ, β and γ.

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
static double	barF(double mu, double beta, double gamma, double x) Computes the complementary distribution function of the fatigue life distribution with parameters μ, β and γ.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(double mu, double beta, double gamma, double x) Computes the fatigue life distribution function with parameters μ, β and γ.
double	density(double x) Returns f (x), the density evaluated at x.
static double	density(double mu, double beta, double gamma, double x) Computes the density for the fatigue life distribution with parameters μ, β and γ.
double	getBeta() Returns the parameter β of this object.
double	getGamma() Returns the parameter γ of this object.
double	getMean() Returns the mean.
static double	getMean(double mu, double beta, double gamma) Computes and returns the mean E[X] = μ + β(1 + γ2/2) of the fatigue life distribution with parameters μ, β and γ.
static double[]	getMLE(double[] x, int n, double mu) Estimates the parameters (μ, β, γ) of the fatigue life distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
double	getMu() Returns the parameter μ of this object.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation.
static double	getStandardDeviation(double mu, double beta, double gamma) Computes and returns the standard deviation of the fatigue life distribution with parameters μ, β and γ.
double	getVariance() Returns the variance.
static double	getVariance(double mu, double beta, double gamma) Computes and returns the variance Var[X] = β2γ2(1 + 5γ2/4) of the fatigue life distribution with parameters μ, β and γ.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(double mu, double beta, double gamma, double u) Computes the inverse of the fatigue life distribution with parameters μ, β and γ.
void	setParams(double mu, double beta, double gamma) Sets the parameters μ, β and γ of this object.
java.lang.String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

FatigueLifeDist

public FatigueLifeDist(double mu,
                       double beta,
                       double gamma)

Constructs a fatigue life distribution with parameters μ, β and γ.

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density evaluated at x.

Specified by:

density in class ContinuousDistribution

Parameters:

x - value at which the density is evaluated

Returns:

density function evaluated at x

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Parameters:

x - value at which the distribution function is evaluated

Returns:

distribution function evaluated at x

barF

public double barF(double x)

Description copied from class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class ContinuousDistribution

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from class: ContinuousDistribution

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getMean

public double getMean()

Description copied from class: ContinuousDistribution

Returns the mean.

Specified by:

getMean in interface Distribution

Overrides:

getMean in class ContinuousDistribution

Returns:

the mean

getVariance

public double getVariance()

Description copied from class: ContinuousDistribution

Returns the variance.

Specified by:

getVariance in interface Distribution

Overrides:

getVariance in class ContinuousDistribution

Returns:

the variance

getStandardDeviation

public double getStandardDeviation()

Description copied from class: ContinuousDistribution

Returns the standard deviation.

Specified by:

getStandardDeviation in interface Distribution

Overrides:

getStandardDeviation in class ContinuousDistribution

Returns:

the standard deviation

density

public static double density(double mu,
                             double beta,
                             double gamma,
                             double x)

Computes the density for the fatigue life distribution with parameters μ, β and γ.

cdf

public static double cdf(double mu,
                         double beta,
                         double gamma,
                         double x)

Computes the fatigue life distribution function with parameters μ, β and γ.

barF

public static double barF(double mu,
                          double beta,
                          double gamma,
                          double x)

Computes the complementary distribution function of the fatigue life distribution with parameters μ, β and γ.

inverseF

public static double inverseF(double mu,
                              double beta,
                              double gamma,
                              double u)

Computes the inverse of the fatigue life distribution with parameters μ, β and γ.

getMLE

public static double[] getMLE(double[] x,
                              int n,
                              double mu)

Estimates the parameters (μ, β, γ) of the fatigue life distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a three-element array, in regular order: [μ, β, γ].

Parameters:

x - the list of observations to use to evaluate parameters

n - the number of observations to use to evaluate parameters

mu - the location parameter

Returns:

returns the parameters [ hat(β), hat(γ)]

getMean

public static double getMean(double mu,
                             double beta,
                             double gamma)

Computes and returns the mean E[X] = μ + β(1 + γ²/2) of the fatigue life distribution with parameters μ, β and γ.

Returns:

the mean of the fatigue life distribution

getVariance

public static double getVariance(double mu,
                                 double beta,
                                 double gamma)

Computes and returns the variance Var[X] = β²γ²(1 + 5γ²/4) of the fatigue life distribution with parameters μ, β and γ.

Returns:

the variance of the fatigue life distribution

getStandardDeviation

public static double getStandardDeviation(double mu,
                                          double beta,
                                          double gamma)

Computes and returns the standard deviation of the fatigue life distribution with parameters μ, β and γ.

Returns:

the standard deviation of the fatigue life distribution

getBeta

public double getBeta()

Returns the parameter β of this object.

getGamma

public double getGamma()

Returns the parameter γ of this object.

getMu

public double getMu()

Returns the parameter μ of this object.

setParams

public void setParams(double mu,
                      double beta,
                      double gamma)

Sets the parameters μ, β and γ of this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in regular order: [μ, β, γ].

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object