Extends the class ContinuousDistribution for the fatigue life distribution [19] with location parameter \(\mu\), scale parameter \(\beta\) and shape parameter \(\gamma\). More...

Inheritance diagram for umontreal.ssj.probdist.FatigueLifeDist:

Public Member Functions
	FatigueLifeDist (double mu, double beta, double gamma)
	Constructs a fatigue life distribution with parameters \(\mu\),.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getBeta ()
	Returns the parameter \(\beta\) of this object.
double	getGamma ()
	Returns the parameter \(\gamma\) of this object.
double	getMu ()
	Returns the parameter \(\mu\) of this object.
void	setParams (double mu, double beta, double gamma)
	Sets the parameters \(\mu\), \(\beta\) and \(\gamma\) of this object.
double[]	getParams ()
	Return a table containing the parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (double mu, double beta, double gamma, double x)
	Computes the density ( `fFatigueLife` ) for the fatigue life distribution with parameters.
static double	cdf (double mu, double beta, double gamma, double x)
	Computes the fatigue life distribution function with parameters.
static double	barF (double mu, double beta, double gamma, double x)
	Computes the complementary distribution function of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).
static double	inverseF (double mu, double beta, double gamma, double u)
	Computes the inverse of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).
static double[]	getMLE (double[] x, int n, double mu)
	Estimates the parameters ( \(\mu\), \(\beta\), \(\gamma\)) of the fatigue life distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).
static double	getMean (double mu, double beta, double gamma)
	Computes and returns the mean \(E[X] = \mu+ \beta(1 + \gamma^2/2)\) of the fatigue life distribution with parameters.
static double	getVariance (double mu, double beta, double gamma)
	Computes and returns the variance \(\mbox{Var}[X] = \beta^2 \gamma^2 (1 + 5 \gamma^2/4)\) of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).
static double	getStandardDeviation (double mu, double beta, double gamma)
	Computes and returns the standard deviation of the fatigue life distribution with parameters \(\mu\), \(\beta\) and.

Detailed Description

Extends the class ContinuousDistribution for the fatigue life distribution [19] with location parameter \(\mu\), scale parameter \(\beta\) and shape parameter \(\gamma\).

Its density is

\[ f(x) = \left[\frac{\sqrt{\frac{x - \mu}{\beta}} + \sqrt{\frac{\beta}{x - \mu}}}{2\gamma(x - \mu)}\right] \phi\left(\frac{\sqrt{\frac{x - \mu}{\beta}} - \sqrt{\frac{\beta}{x - \mu}}}{\gamma}\right), \qquad\mbox{for } x>\mu, \tag{fFatigueLife} \]

where \(\phi\) is the probability density of the standard normal distribution. The distribution function is given by

\[ F(x) = \Phi\left(\frac{\sqrt{\frac{x - \mu}{\beta}} - \sqrt{\frac{\beta}{x - \mu}}}{\gamma}\right), \qquad\mbox{for } x>\mu, \tag{FFatigueLife} \]

where \(\Phi\) is the standard normal distribution function. Restrictions: \(\beta> 0\), \(\gamma> 0\).

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

Definition at line 55 of file FatigueLifeDist.java.

Constructor & Destructor Documentation

◆ FatigueLifeDist()

umontreal.ssj.probdist.FatigueLifeDist.FatigueLifeDist	(	double	mu,
		double	beta,
		double	gamma )

Constructs a fatigue life distribution with parameters \(\mu\),.

\(\beta\) and \(\gamma\).

Definition at line 96 of file FatigueLifeDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.barF	(	double	mu,
		double	beta,
		double	gamma,
		double	x )

static

Computes the complementary distribution function of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).

Definition at line 168 of file FatigueLifeDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 108 of file FatigueLifeDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.cdf	(	double	mu,
		double	beta,
		double	gamma,
		double	x )

static

Computes the fatigue life distribution function with parameters.

\(\mu\), \(\beta\) and \(\gamma\).

Definition at line 153 of file FatigueLifeDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Definition at line 104 of file FatigueLifeDist.java.

◆ density() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.density	(	double	mu,
		double	beta,
		double	gamma,
		double	x )

static

Computes the density ( fFatigueLife ) for the fatigue life distribution with parameters.

\(\mu\), \(\beta\) and \(\gamma\).

Definition at line 134 of file FatigueLifeDist.java.

◆ density() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.density ( double x )

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

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 100 of file FatigueLifeDist.java.

◆ getBeta()

double umontreal.ssj.probdist.FatigueLifeDist.getBeta ( )

Returns the parameter \(\beta\) of this object.

Definition at line 308 of file FatigueLifeDist.java.

◆ getGamma()

double umontreal.ssj.probdist.FatigueLifeDist.getGamma ( )

Returns the parameter \(\gamma\) of this object.

Definition at line 315 of file FatigueLifeDist.java.

◆ getMean() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.getMean ( )

Returns the mean.

Returns: the mean

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 116 of file FatigueLifeDist.java.

◆ getMean() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.getMean	(	double	mu,
		double	beta,
		double	gamma )

static

Computes and returns the mean \(E[X] = \mu+ \beta(1 + \gamma^2/2)\) of the fatigue life distribution with parameters.

\(\mu\), \(\beta\) and \(\gamma\).

Returns: the mean of the fatigue life distribution

Definition at line 270 of file FatigueLifeDist.java.

◆ getMLE()

double[] umontreal.ssj.probdist.FatigueLifeDist.getMLE	(	double[]	x,
		int	n,
		double	mu )

static

Estimates the parameters ( \(\mu\), \(\beta\), \(\gamma\)) 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: [ \(\mu\), \(\beta\), \(\gamma\)]. The estimate of the parameters is given by maximizing numerically the log-likelihood function, using the Uncmin package [203],

[224] .

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 [ \(\hat{\beta}\), \(\hat{\gamma}\)]

Definition at line 217 of file FatigueLifeDist.java.

◆ getMu()

double umontreal.ssj.probdist.FatigueLifeDist.getMu ( )

Returns the parameter \(\mu\) of this object.

Definition at line 322 of file FatigueLifeDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.FatigueLifeDist.getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(\mu\), \(\beta\), \(\gamma\)].

Implements umontreal.ssj.probdist.Distribution.

Definition at line 345 of file FatigueLifeDist.java.

◆ getStandardDeviation() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.getStandardDeviation ( )

Returns the standard deviation.

Returns: the standard deviation

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 124 of file FatigueLifeDist.java.

◆ getStandardDeviation() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.getStandardDeviation	(	double	mu,
		double	beta,
		double	gamma )

static

Computes and returns the standard deviation of the fatigue life distribution with parameters \(\mu\), \(\beta\) and.

\(\gamma\).

Returns: the standard deviation of the fatigue life distribution

Definition at line 301 of file FatigueLifeDist.java.

◆ getVariance() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.getVariance ( )

Returns the variance.

Returns: the variance

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 120 of file FatigueLifeDist.java.

◆ getVariance() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.getVariance	(	double	mu,
		double	beta,
		double	gamma )

static

Computes and returns the variance \(\mbox{Var}[X] = \beta^2 \gamma^2 (1 + 5 \gamma^2/4)\) of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).

Returns: the variance of the fatigue life distribution

Definition at line 286 of file FatigueLifeDist.java.

◆ inverseF() [1/2]

double umontreal.ssj.probdist.FatigueLifeDist.inverseF	(	double	mu,
		double	beta,
		double	gamma,
		double	u )

static

Computes the inverse of the fatigue life distribution with parameters \(\mu\), \(\beta\) and \(\gamma\).

Definition at line 183 of file FatigueLifeDist.java.

◆ inverseF() [2/2]

double umontreal.ssj.probdist.FatigueLifeDist.inverseF ( double u )

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 112 of file FatigueLifeDist.java.

◆ setParams()

void umontreal.ssj.probdist.FatigueLifeDist.setParams	(	double	mu,
		double	beta,
		double	gamma )

Sets the parameters \(\mu\), \(\beta\) and \(\gamma\) of this object.

Definition at line 329 of file FatigueLifeDist.java.

◆ toString()

String umontreal.ssj.probdist.FatigueLifeDist.toString ( )

Returns a String containing information about the current distribution.

Definition at line 353 of file FatigueLifeDist.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/probdist/FatigueLifeDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ FatigueLifeDist()

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density() [1/2]

◆ density() [2/2]

◆ getBeta()

◆ getGamma()

◆ getMean() [1/2]

◆ getMean() [2/2]

◆ getMLE()

◆ getMu()

◆ getParams()

◆ getStandardDeviation() [1/2]

◆ getStandardDeviation() [2/2]

◆ getVariance() [1/2]

◆ getVariance() [2/2]

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ setParams()

◆ toString()