SSJ  3.3.1
Stochastic Simulation in Java
Classes | Public Member Functions | Static Public Member Functions | Protected Attributes | List of all members
FatigueLifeDist Class Reference

Extends the class ContinuousDistribution for the fatigue life distribution [20]  with location parameter \(\mu\), scale parameter \(\beta\) and shape parameter \(\gamma\). More...

Inheritance diagram for FatigueLifeDist:
[legend]
Collaboration diagram for FatigueLifeDist:
[legend]

Public Member Functions

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

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 \(\mu\), \(\beta\) and \(\gamma\).
 
static double cdf (double mu, double beta, double gamma, double x)
 Computes the fatigue life distribution function with parameters \(\mu\), \(\beta\) and \(\gamma\).
 
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 \(x[i]\), \(i = 0, 1,…, n-1\). More...
 
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 \(\mu\), \(\beta\) and \(\gamma\). More...
 
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 \(\gamma\). More...
 
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 \(\gamma\). More...
 

Protected Attributes

double mu
 
double beta
 
double gamma
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 

Detailed Description

Extends the class ContinuousDistribution for the fatigue life distribution [20]  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.

Member Function Documentation

◆ barF()

double barF ( double  x)

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters
xvalue at which the complementary distribution function is evaluated
Returns
complementary distribution function evaluated at x

Implements Distribution.

◆ cdf()

double cdf ( double  x)

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

Parameters
xvalue at which the distribution function is evaluated
Returns
distribution function evaluated at x

Implements Distribution.

◆ getMean()

static double 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

◆ getMLE()

static double [] 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 [211], [233] .

Parameters
xthe list of observations to use to evaluate parameters
nthe number of observations to use to evaluate parameters
muthe location parameter
Returns
returns the parameters [ \(\hat{\beta}\), \(\hat{\gamma}\)]

◆ getParams()

double [] getParams ( )

Return a table containing the parameters of the current distribution.

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

Implements Distribution.

◆ getStandardDeviation()

static double 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

◆ getVariance()

static double 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

◆ inverseF()

double inverseF ( double  u)

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters
uvalue in the interval \((0,1)\) for which the inverse distribution function is evaluated
Returns
the inverse distribution function evaluated at u

Implements Distribution.


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