smile.stat.distribution

Class BernoulliDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.DiscreteDistribution

smile.stat.distribution.BernoulliDistribution

All Implemented Interfaces:

java.io.Serializable, Distribution

public class BernoulliDistribution
extends DiscreteDistribution

Bernoulli distribution is a discrete probability distribution, which takes value 1 with success probability p and value 0 with failure probability q = 1 - p.

Although Bernoulli distribution belongs to exponential family, we don't implement DiscreteExponentialFamily interface here since it is impossible and meaningless to estimate a mixture of Bernoulli distributions.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	p Probability of success.
double	q Probability of failure.

Constructor Summary

Constructors

Constructor and Description
BernoulliDistribution(boolean[] data) Construct an Bernoulli from the given samples.
BernoulliDistribution(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 BernoulliDistribution	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.
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.
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, sd

Field Detail

p

public final double p

Probability of success.

q

public final double q

Probability of failure.

Constructor Detail

BernoulliDistribution

public BernoulliDistribution(double p)

Constructor.

Parameters:

p - the probability of success.

BernoulliDistribution

public BernoulliDistribution(boolean[] data)

Construct an Bernoulli from the given samples. Parameter will be estimated from the data by MLE.

Parameters:

data - the boolean array to indicate if the i-th trail success.

Method Detail

fit

public static BernoulliDistribution fit(int[] data)

Estimates the distribution parameters by MLE.

Parameters:

data - data[i] == 1 if the i-th trail is success. Otherwise 0.

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.

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

variance

public double variance()

Description copied from interface: Distribution

The variance of distribution.

entropy

public double entropy()

Description copied from interface: Distribution

Shannon entropy of the 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.

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.

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.