FatigueLifeDist (Java Libraries for Stochastic Simulation)

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

Methods
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.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int n, double mu)` Deprecated.
`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)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int n,
                                               double mu)
```
    Deprecated.
    
    Same as getMLE.
  - 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

Class FatigueLifeDist

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

FatigueLifeDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getMean

getVariance

getStandardDeviation

getBeta

getGamma

getMu

setParams

getParams

toString