WeibullDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.WeibullDist

All Implemented Interfaces:

Distribution
```
public class WeibullDist
extends ContinuousDistribution
```
This class extends the class ContinuousDistribution for the Weibull distribution with shape parameter α > 0, location parameter δ, and scale parameter λ > 0. The density function is

f (x) = αλ^α(x - δ)^α-1e^{-(λ(x-δ))^α}        for x > δ.
the distribution function is

F(x) = 1 - e^{-(λ(x-δ))^α}        for x > δ,
and the inverse distribution function is

F^-1(u) = (- ln(1 - u))^1/α/λ + δ        for 0 <= u < 1.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description
`WeibullDist(double alpha)` Constructs a `WeibullDist` object with parameters α = `alpha`, λ = 1, and δ = 0.
`WeibullDist(double alpha, double lambda, double delta)` Constructs a `WeibullDist` object with parameters α = `alpha`, λ = `lambda`, and δ = `delta`.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(double alpha, double x)` Same as `barF (alpha, 1, 0, x)`.
`static double`	`barF(double alpha, double lambda, double delta, double x)` Computes the complementary distribution function.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(double alpha, double x)` Same as `cdf (alpha, 1, 0, x)`.
`static double`	`cdf(double alpha, double lambda, double delta, double x)` Computes the distribution function.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(double alpha, double x)` Same as `density (alpha, 1, 0, x)`.
`static double`	`density(double alpha, double lambda, double delta, double x)` Computes the density function.
`double`	`getAlpha()` Returns the parameter α.
`double`	`getDelta()` Returns the parameter δ.
`static WeibullDist`	`getInstanceFromMLE(double[] x, int n)` Creates a new instance of a Weibull distribution with parameters α, λ and δ = 0 estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
`double`	`getLambda()` Returns the parameter λ.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int n)` Deprecated.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(double alpha, double lambda, double delta)` Computes and returns the mean of the Weibull distribution with parameters α, λ and δ.
`static double[]`	`getMLE(double[] x, int n)` Estimates the parameters (α, λ) of the Weibull distribution, assuming that δ = 0, using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(double alpha, double lambda, double delta)` Computes and returns the standard deviation of the Weibull distribution with parameters α, λ and δ.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double alpha, double lambda, double delta)` Computes and returns the variance of the Weibull distribution with parameters α, λ and δ.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(double alpha, double x)` Same as `inverseF (alpha, 1, 0, x)`.
`static double`	`inverseF(double alpha, double lambda, double delta, double u)` Computes the inverse of the distribution function.
`void`	`setParams(double alpha, double lambda, double delta)` Sets the parameters α, λ and δ for 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
  - WeibullDist
```
public WeibullDist(double alpha)
```
    Constructs a WeibullDist object with parameters α = alpha, λ = 1, and δ = 0.
  - WeibullDist
```
public WeibullDist(double alpha,
           double lambda,
           double delta)
```
    Constructs a WeibullDist object with parameters α = alpha, λ = lambda, and δ = delta.
- 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 alpha,
             double lambda,
             double delta,
             double x)
```
    Computes the density function.
  - density
```
public static double density(double alpha,
             double x)
```
    Same as density (alpha, 1, 0, x).
  - cdf
```
public static double cdf(double alpha,
         double lambda,
         double delta,
         double x)
```
    Computes the distribution function.
  - cdf
```
public static double cdf(double alpha,
         double x)
```
    Same as cdf (alpha, 1, 0, x).
  - barF
```
public static double barF(double alpha,
          double lambda,
          double delta,
          double x)
```
    Computes the complementary distribution function.
  - barF
```
public static double barF(double alpha,
          double x)
```
    Same as barF (alpha, 1, 0, x).
  - inverseF
```
public static double inverseF(double alpha,
              double lambda,
              double delta,
              double u)
```
    Computes the inverse of the distribution function.
  - inverseF
```
public static double inverseF(double alpha,
              double x)
```
    Same as inverseF (alpha, 1, 0, x).
  - getMLE
```
public static double[] getMLE(double[] x,
              int n)
```
    Estimates the parameters (α, λ) of the Weibull distribution, assuming that δ = 0, using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [α, λ].
    
    Parameters:
    x - the list of observations to use to evaluate parameters
    n - the number of observations to use to evaluate parameters
    
    Returns:
    returns the parameter [ hat(α), hat(λ), hat(δ) = 0]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static WeibullDist getInstanceFromMLE(double[] x,
                             int n)
```
    Creates a new instance of a Weibull distribution with parameters α, λ and δ = 0 estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
    
    Parameters:
    x - the list of observations to use to evaluate parameters
    n - the number of observations to use to evaluate parameters
  - getMean
```
public static double getMean(double alpha,
             double lambda,
             double delta)
```
    Computes and returns the mean of the Weibull distribution with parameters α, λ and δ.
    
    Returns:
    the mean of the Weibull distribution E[X] = δ + Γ(1 + 1/α)/λ
  - getVariance
```
public static double getVariance(double alpha,
                 double lambda,
                 double delta)
```
    Computes and returns the variance of the Weibull distribution with parameters α, λ and δ.
    
    Returns:
    the variance of the Weibull distribution Var[X] = 1/λ²| Γ(2/α +1) - Γ²(1/α + 1)|
  - getStandardDeviation
```
public static double getStandardDeviation(double alpha,
                          double lambda,
                          double delta)
```
    Computes and returns the standard deviation of the Weibull distribution with parameters α, λ and δ.
    
    Returns:
    the standard deviation of the Weibull distribution
  - getAlpha
```
public double getAlpha()
```
    Returns the parameter α.
  - getLambda
```
public double getLambda()
```
    Returns the parameter λ.
  - getDelta
```
public double getDelta()
```
    Returns the parameter δ.
  - setParams
```
public void setParams(double alpha,
             double lambda,
             double delta)
```
    Sets the parameters α, λ and δ for this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in regular order: [α, λ, δ].
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class WeibullDist

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

WeibullDist

WeibullDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

density

cdf

cdf

barF

barF

inverseF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getAlpha

getLambda

getDelta

setParams

getParams

toString