umontreal.iro.lecuyer.probdist
Class WeibullDist

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

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

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(double alpha, double x) Same as barF (alpha, 1.0, 0.0, x).
static double	barF(double alpha, double lambda, double delta, double x) Computes the complementary distribution function.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(double alpha, double x) Same as cdf (alpha, 1.0, 0.0, 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 of X evaluated at x.
static double	density(double alpha, double x) Same as density (alpha, 1.0, 0.0, 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.
double	getLambda() Returns the parameter λ.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(double alpha, double x) Same as inverseF (alpha, 1.0, 0.0, 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.

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

inverseBisection, inverseBrent

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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

Computes and 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 interface: Distribution

Returns 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 interface: Distribution

Computes and returns the inverse distribution function F^-1(u), defined in.

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value in the interval (0, 1) for which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

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, 0.0, 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, 0.0, 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, 0.0, 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, 0.0, x).

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.