Package dev.nm.stat.distribution.univariate

Class BinomialDistribution

java.lang.Object

dev.nm.stat.distribution.univariate.BinomialDistribution

All Implemented Interfaces:

ProbabilityDistribution

public class BinomialDistribution
extends Object
implements ProbabilityDistribution

The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. For N much larger than n, the binomial distribution is a good approximation of hypergeometric distribution.

See Also:

Wikipedia: Binomial distribution

Constructor Summary

Constructors

Constructor	Description
BinomialDistribution(int n, double p)	Construct a Binomial distribution.

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Gets the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x)	This is the probability mass function.
double	entropy()	Gets the entropy of this distribution.
double	kurtosis()	Gets the excess kurtosis of this distribution.
double	mean()	Gets the mean of this distribution.
double	median()	Gets the median of this distribution.
double	moment(double t)	The moment generating function is the expected value of etX.
double	quantile(double u)	Gets the quantile, the inverse of the cumulative distribution function.
double	skew()	Gets the skewness of this distribution.
double	variance()	Gets the variance of this distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

BinomialDistribution

public BinomialDistribution(int n,
                            double p)

Construct a Binomial distribution.

Parameters:

n - the number of trials, a natural number

p - the success probability in each trial, [0, 1]

Method Detail

mean

public double mean()

Description copied from interface: ProbabilityDistribution

Gets the mean of this distribution.

Specified by:

mean in interface ProbabilityDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

public double median()

Gets the median of this distribution.

The result is rounded rounded down to an integer.

Specified by:

median in interface ProbabilityDistribution

Returns:

median

See Also:

Wikipedia: Median

variance

public double variance()

Description copied from interface: ProbabilityDistribution

Gets the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

public double skew()

Description copied from interface: ProbabilityDistribution

Gets the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Description copied from interface: ProbabilityDistribution

Gets the excess kurtosis of this distribution.

Specified by:

kurtosis in interface ProbabilityDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

cdf

public double cdf(double x)

Gets the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

x - the number of success trials, an integer; rounded down to the closest integer if x is not an integer

Returns:

cdf(x)

See Also:

Wikipedia: Cumulative distribution function

quantile

public double quantile(double u)

Gets the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.

 F-1(u) = x, such that
 Pr(X ≤ x) = u
 

This may not always exist.

Uses the Cornish-Fisher Expansion to include a skewness correction to a normal approximation. This gives an initial value which never seems to be off by more than 1 or 2. A search is then conducted of values close to this initial start point.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - a quantile

Returns:

qbinom(u)

See Also:

qbinom

density

public double density(double x)

This is the probability mass function.

Specified by:

density in interface ProbabilityDistribution

Parameters:

x - the number of success trials, an integer; rounded down to the closest integer if x is not an integer

Returns:

pmf(x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

entropy

public double entropy()

Description copied from interface: ProbabilityDistribution

Gets the entropy of this distribution.

Specified by:

entropy in interface ProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

moment

public double moment(double t)

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of e^tX. That is,

E(e^tX)

This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

t - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function