SSJ
V. labo.

umontreal.iro.lecuyer.probdist
Class FatigueLifeDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.FatigueLifeDist
All Implemented Interfaces:
Distribution

public class FatigueLifeDist
extends ContinuousDistribution

FatigueLifeDist

Extends the class ContinuousDistribution for the fatigue life distribution[#!tBIR69a!#] 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
FatigueLifeDist(double mu, double beta, double gamma)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double mu, double beta, double gamma, double x)
          .
 double cdf(double x)
          .
static double cdf(double mu, double beta, double gamma, double x)
          .
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double mu, double beta, double gamma, double x)
          .
 double getBeta()
          .
 double getGamma()
          .
 double getMean()
          Returns the mean.
static double getMean(double mu, double beta, double gamma)
          .
static double[] getMLE(double[] x, int n, double mu)
          .
 double getMu()
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double mu, double beta, double gamma)
          .
 double getVariance()
          Returns the variance.
static double getVariance(double mu, double beta, double gamma)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double mu, double beta, double gamma, double u)
          .
 void setParams(double mu, double beta, double gamma)
          .
 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)
. \begin{tabb}
 Constructs a fatigue life distribution with parameters
 $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}

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
. \begin{tabb}Returns the distribution function $F(x)$.
 \end{tabb}
xvalue at which the distribution function is evaluated 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)
. \begin{tabb}Computes the density for the
 fatigue life distribution with parameters $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}


cdf

public static double cdf(double mu,
                         double beta,
                         double gamma,
                         double x)
. \begin{tabb}
 Computes the fatigue life distribution
 function with parameters $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}


barF

public static double barF(double mu,
                          double beta,
                          double gamma,
                          double x)
. \begin{tabb}
 Computes the complementary distribution function of the
 fatigue life distribution with parameters $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}


inverseF

public static double inverseF(double mu,
                              double beta,
                              double gamma,
                              double u)
. \begin{tabb}
 Computes the inverse of the fatigue life distribution
 with parameters $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}


getMLE

public static double[] getMLE(double[] x,
                              int n,
                              double mu)
. \begin{tabb}
 Estimates the parameters ($\mu$, $\beta$, $\gamma$) of the fatigue...
 ... function, using the Uncmin package\cite{iSCHa,iVERa}.
 \end{detailed}\end{tabb}
xthe list of observations to use to evaluate parameters nthe number of observations to use to evaluate parameters muthe location parameter returns the parameters [ $ \hat{{\beta}}$, $ \hat{{\gamma}}$]


getMean

public static double getMean(double mu,
                             double beta,
                             double gamma)
. \begin{tabb}Computes and returns the mean
 $E[X] = \mu + \beta(1 + \gamma^2/2)$
 ...
 ...ta$\ and $\gamma$.
 \return{the mean of the fatigue life distribution}
 \end{tabb}


getVariance

public static double getVariance(double mu,
                                 double beta,
                                 double gamma)
. \begin{tabb}Computes and returns the variance
 $\mbox{Var}[X] = \beta^2 \gamma^2...
 ... and $\gamma$.
 \return{the variance of the fatigue life distribution}
 \end{tabb}


getStandardDeviation

public static double getStandardDeviation(double mu,
                                          double beta,
                                          double gamma)
. \begin{tabb}Computes and returns the standard deviation
 of the fatigue life distribution
 with parameters $\mu$, $\beta$\ and $\gamma$.
 \end{tabb}
the standard deviation of the fatigue life distribution


getBeta

public double getBeta()
. \begin{tabb}Returns the parameter $\beta$\ of this object.
 \end{tabb}


getGamma

public double getGamma()
. \begin{tabb}Returns the parameter $\gamma$\ of this object.
 \end{tabb}


getMu

public double getMu()
. \begin{tabb}Returns the parameter $\mu$\ of this object.
 \end{tabb}


setParams

public void setParams(double mu,
                      double beta,
                      double gamma)
. \begin{tabb}
 Sets the parameters $\mu$, $\beta$\ and $\gamma$\ of this object.
 \end{tabb}


getParams

public double[] getParams()
. \begin{tabb}
 Return a table containing the parameters of the current distribution.
 This table is put in regular order: [$\mu$, $\beta$, $\gamma$].
 \end{tabb}

 


toString

public String toString()
. \begin{hide}
 \par
 \begin{tabb}
 Returns a \texttt{String} containing information about the current distribution.
 \end{tabb}\end{hide}

Overrides:
toString in class Object

SSJ
V. labo.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.