smile.stat.distribution

Class GeometricDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.DiscreteDistribution

smile.stat.distribution.GeometricDistribution

All Implemented Interfaces:

DiscreteExponentialFamily, Distribution

public class GeometricDistribution
extends DiscreteDistribution
implements DiscreteExponentialFamily

The geometric distribution is a discrete probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set {1, 2, 3, …}. Sometimes, people define that the probability distribution of the number Y = X - 1 of failures before the first success, supported on the set {0, 1, 2, 3, …}. To reduce the confusion, we denote the later as shifted geometric distribution. If the probability of success on each trial is p, then the probability that the k-th trial (out of k trials) is the first success is Pr(X = k) = (1 - p)^k-1 p.

Like its continuous analogue (the exponential distribution), the geometric distribution is memoryless. That means that if you intend to repeat an experiment until the first success, then, given that the first success has not yet occurred, the conditional probability distribution of the number of additional trials does not depend on how many failures have been observed. The geometric distribution is in fact the only memoryless discrete distribution.

Among all discrete probability distributions supported on {1, 2, 3, …} with given expected value μ, the geometric distribution X with parameter p = 1/μ is the one with the largest entropy.

See Also:

ShiftedGeometricDistribution

Constructor Summary

Constructors

Constructor and Description
GeometricDistribution(double p) Constructor.
GeometricDistribution(int[] data) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double k) Cumulative distribution function.
double	entropy() Shannon entropy.
double	getProb() Returns the probability of success.
double	logp(int k) The probability mass function in log scale.
DiscreteMixture.Component	M(int[] x, double[] posteriori) The M step in the EM algorithm, which depends the specific distribution.
double	mean() The mean of distribution.
int	npara() The number of parameters of the distribution.
double	p(int k) The probability mass function.
double	quantile(double p) The quantile, the probability to the left of quantile is p.
double	rand() Generates a random number following this distribution.
double	sd() The standard deviation of distribution.
java.lang.String	toString()
double	var() The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution

likelihood, logLikelihood, logp, p

Methods inherited from class smile.stat.distribution.AbstractDistribution

likelihood, logLikelihood

Methods inherited from class java.lang.Object

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

Constructor Detail

GeometricDistribution

public GeometricDistribution(double p)

Constructor.

Parameters:

p - the probability of success.

GeometricDistribution

public GeometricDistribution(int[] data)

Constructor. Parameter will be estimated from the data by MLE.

Method Detail

getProb

public double getProb()

Returns the probability of success.

npara

public int npara()

Description copied from interface: Distribution

The number of parameters of the distribution.

Specified by:

npara in interface Distribution

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

Specified by:

mean in interface Distribution

var

public double var()

Description copied from interface: Distribution

The variance of distribution.

Specified by:

var in interface Distribution

sd

public double sd()

Description copied from interface: Distribution

The standard deviation of distribution.

Specified by:

sd in interface Distribution

entropy

public double entropy()

Shannon entropy. Not supported.

Specified by:

entropy in interface Distribution

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

rand

public double rand()

Description copied from interface: Distribution

Generates a random number following this distribution.

Specified by:

rand in interface Distribution

p

public double p(int k)

Description copied from class: DiscreteDistribution

The probability mass function.

Specified by:

p in class DiscreteDistribution

logp

public double logp(int k)

Description copied from class: DiscreteDistribution

The probability mass function in log scale.

Specified by:

logp in class DiscreteDistribution

cdf

public double cdf(double k)

Description copied from interface: Distribution

Cumulative distribution function. That is the probability to the left of x.

Specified by:

cdf in interface Distribution

quantile

public double quantile(double p)

Description copied from interface: Distribution

The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.

Specified by:

quantile in interface Distribution

M

public DiscreteMixture.Component M(int[] x,
                                   double[] posteriori)

Description copied from interface: DiscreteExponentialFamily

The M step in the EM algorithm, which depends the specific distribution.

Specified by:

M in interface DiscreteExponentialFamily

Parameters:

x - the input data for estimation

posteriori - the posteriori probability.

Returns:

the (unnormalized) weight of this distribution in the mixture.