smile.stat.distribution

Class ShiftedGeometricDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.DiscreteDistribution

smile.stat.distribution.ShiftedGeometricDistribution

All Implemented Interfaces:

java.io.Serializable, DiscreteExponentialFamily, Distribution

public class ShiftedGeometricDistribution
extends DiscreteDistribution
implements DiscreteExponentialFamily

The "shifted" geometric distribution is a discrete probability distribution of the number of failures before the first success, supported on the set {0, 1, 2, 3, …}. 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 p
 

.

See Also:

GeometricDistribution, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	p The probability of success.

Constructor Summary

Constructors

Constructor and Description
ShiftedGeometricDistribution(double p) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double k) Cumulative distribution function.
double	entropy() Shannon entropy of the distribution.
static ShiftedGeometricDistribution	fit(int[] data) Estimates the distribution parameters by MLE.
int	length() The number of parameters of the distribution.
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.
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	variance() The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution

likelihood, logLikelihood, logp, p, quantile, randi, randi

Methods inherited from class smile.stat.distribution.AbstractDistribution

inverseTransformSampling, quantile, quantile, rejection

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface smile.stat.distribution.Distribution

likelihood, logLikelihood, rand

Field Detail

p

public final double p

The probability of success.

Constructor Detail

ShiftedGeometricDistribution

public ShiftedGeometricDistribution(double p)

Constructor.

Parameters:

p - the probability of success.

Method Detail

fit

public static ShiftedGeometricDistribution fit(int[] data)

Estimates the distribution parameters by MLE.

length

public int length()

Description copied from interface: Distribution

The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.

Specified by:

length in interface Distribution

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

Specified by:

mean in interface Distribution

variance

public double variance()

Description copied from interface: Distribution

The variance of distribution.

Specified by:

variance 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()

Description copied from interface: Distribution

Shannon entropy of the distribution.

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.