umontreal.iro.lecuyer.probdist
Class GeometricDist

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

All Implemented Interfaces:

Distribution

public class GeometricDist
extends DiscreteDistributionInt

Extends the class DiscreteDistributionInt for the geometric distribution with parameter p, where 0 < p < 1. Its mass function is

p(x) = p (1 - p)^x, for x = 0, 1, 2,…

The distribution function is given by

F(x) = 1 - (1 - p)^x+1, for x = 0, 1, 2,…

and its inverse is

F^-1(u) = floor(ln(1 - u)/ln(1 - p)), for 0 <= u < 1.

Field Summary

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

EPSILON

Constructor Summary

GeometricDist(double p)
Constructs a geometric distribution with parameter p.

Method Summary

static double	barF(double p, int x) Computes the complementary distribution function.
double	barF(int x) Returns bar(F)(x), the complementary distribution function.
static double	cdf(double p, int x) Computes the distribution function F(x).
double	cdf(int x) Returns the distribution function F evaluated at x (see).
static GeometricDist	getInstanceFromMLE(int[] x, int n) Creates a new instance of a geometric distribution with parameter p estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
double	getMean() Returns the mean of the distribution function.
static double	getMean(double p) Computes and returns the mean E[X] = (1 - p)/p of the geometric distribution with parameter p.
static double[]	getMLE(int[] x, int n) Estimates the parameter p of the geometric distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
double	getP() Returns the p associated with this object.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation of the distribution function.
static double	getStandardDeviation(double p) Computes and returns the standard deviation of the geometric distribution with parameter p.
double	getVariance() Returns the variance of the distribution function.
static double	getVariance(double p) Computes and returns the variance Var[X] = (1 - p)/p2 of the geometric distribution with parameter p.
static int	inverseF(double p, double u) Computes the inverse of the geometric distribution.
int	inverseFInt(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
static double	prob(double p, int x) Computes the geometric probability p(x).
double	prob(int x) Returns p(x), the probability of x.
void	setP(double p) Resets the value of p associated with this object.
String	toString()

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

barF, cdf, getXinf, getXsup, inverseF

Methods inherited from class java.lang.Object

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

Constructor Detail

GeometricDist

public GeometricDist(double p)

Constructs a geometric distribution with parameter p.

Method Detail

prob

public double prob(int x)

Description copied from class: DiscreteDistributionInt

Returns p(x), the probability of x.

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. See the WARNING above.

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

inverseFInt

public int inverseFInt(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:

inverseFInt 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

getMean

public double getMean()

Description copied from interface: Distribution

Returns the mean of the distribution function.

getVariance

public double getVariance()

Description copied from interface: Distribution

Returns the variance of the distribution function.

getStandardDeviation

public double getStandardDeviation()

Description copied from interface: Distribution

Returns the standard deviation of the distribution function.

prob

public static double prob(double p,
                          int x)

Computes the geometric probability p(x).

cdf

public static double cdf(double p,
                         int x)

Computes the distribution function F(x).

barF

public static double barF(double p,
                          int x)

Computes the complementary distribution function. WARNING: The complementary distribution function is defined as bar(F)(x) = P[X >= x].

inverseF

public static int inverseF(double p,
                           double u)

Computes the inverse of the geometric distribution.

getMLE

public static double[] getMLE(int[] x,
                              int n)

Estimates the parameter p of the geometric distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimate is returned in element 0 of the returned array.

Parameters:

x - the list of observations used to evaluate parameters

n - the number of observations used to evaluate parameters

Returns:

returns the parameter [hat(p)]

getInstanceFromMLE

public static GeometricDist getInstanceFromMLE(int[] x,
                                               int n)

Creates a new instance of a geometric distribution with parameter p 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 p)

Computes and returns the mean E[X] = (1 - p)/p of the geometric distribution with parameter p.

Returns:

the mean of the geometric distribution E[X] = (1 - p)/p

getVariance

public static double getVariance(double p)

Computes and returns the variance Var[X] = (1 - p)/p² of the geometric distribution with parameter p.

Returns:

the variance of the Geometric distribution Var[X] = (1 - p)/p²

getStandardDeviation

public static double getStandardDeviation(double p)

Computes and returns the standard deviation of the geometric distribution with parameter p.

Returns:

the standard deviation of the geometric distribution

getP

public double getP()

Returns the p associated with this object.

setP

public void setP(double p)

Resets the value of p associated with this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution.

toString

public String toString()

Overrides:

toString in class Object