umontreal.iro.lecuyer.probdist
Class LogarithmicDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
      umontreal.iro.lecuyer.probdist.LogarithmicDist

public class LogarithmicDist
extends DiscreteDistributionInt

Extends the class DiscreteDistributionInt for the logarithmic distribution. It has shape parameter θ, where 0 < θ < 1. Its mass function is

p(x) = - 1/log(1 - θ)θ^x/x for x = 1, 2,...

Its distribution function is

F(x) = -1/log(1-θ)∑_i=1^xθⁱ/i, & for x > 0.

Field Summary

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

EPSILON

Constructor Summary

LogarithmicDist(double theta)
Constructs a logarithmic distribution with parameter θ.

Method Summary

static double	barF(double theta, int x) Computes the complementary distribution function bar(F)(x).
double	barF(int x) Returns bar(F)(x), the complementary distribution function.
static double	cdf(double theta, int x) Computes the distribution function F(x).
double	cdf(int x) Returns the distribution function F evaluated at x (see).
double	getTheta() Returns the θ associated with this object.
int	inverseF(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
static int	inverseF(double theta, double u)
static double	prob(double theta, int x) Computes the probability mass function p(x).
double	prob(int x) Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
void	setTheta(double theta) Sets the θ associated with this object.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LogarithmicDist

public LogarithmicDist(double theta)

Constructs a logarithmic distribution with parameter θ.

Method Detail

prob

public double prob(int x)

Description copied from class: DiscreteDistributionInt

Returns p(x), the probability of x, which should be a real number in the interval [0, 1].

Specified by:

prob in class DiscreteDistributionInt

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

cdf

public double cdf(int x)

Description copied from class: DiscreteDistributionInt

Returns the distribution function F evaluated at x (see).

Specified by:

cdf in class DiscreteDistributionInt

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the distribution function evaluated at x

barF

public double barF(int x)

Description copied from class: DiscreteDistributionInt

Returns bar(F)(x), the complementary distribution function.

Overrides:

barF in class DiscreteDistributionInt

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x

inverseF

public int inverseF(double u)

Description copied from class: DiscreteDistributionInt

Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. The default implementation uses binary search.

Overrides:

inverseF in class DiscreteDistributionInt

Parameters:

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

Returns:

the inverse distribution function evaluated at u

prob

public static double prob(double theta,
                          int x)

Computes the probability mass function p(x).

cdf

public static double cdf(double theta,
                         int x)

Computes the distribution function F(x).

barF

public static double barF(double theta,
                          int x)

Computes the complementary distribution function bar(F)(x).

inverseF

public static int inverseF(double theta,
                           double u)

getTheta

public double getTheta()

Returns the θ associated with this object.

setTheta

public void setTheta(double theta)

Sets the θ associated with this object.