dev.nm.stat.distribution.univariate

Class GammaDistribution

java.lang.Object

dev.nm.stat.distribution.univariate.GammaDistribution

All Implemented Interfaces:

ProbabilityDistribution

public class GammaDistribution
extends Object
implements ProbabilityDistribution

This gamma distribution, when k is an integer, is the distribution of the sum of k independent exponentially distributed random variables, each of which has a mean of θ (which is equivalent to a rate parameter of \(\theta ^{-1}\)).

The R equivalent functions are dgamma, pgamma, qgamma, rgamma.

See Also:

Wikipedia: Gamma distribution distribution

Constructor Summary

Constructors

Constructor and Description
GammaDistribution(double k, double theta) Construct a Gamma distribution.

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Gets the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x) The density function, which, if exists, is the derivative of F.
double	entropy() Deprecated. Not supported yet.
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 \(e^{tX}\).
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

GammaDistribution

public GammaDistribution(double k,
                         double theta)

Construct a Gamma distribution.

Parameters:

k - the shape parameter

theta - the scale parameter

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()

Description copied from interface: ProbabilityDistribution

Gets the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the 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

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

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)

cdf

public double cdf(double x)

Description copied from interface: ProbabilityDistribution

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

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

quantile

public double quantile(double u)

Description copied from interface: ProbabilityDistribution

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. \[ \begin{gathered} F^{-1}(u) = x, such that \\ Pr(X \le x) = u \end{gathered} \] This may not always exist.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - u, a quantile

Returns:

\(F^{-1}(u)\)

See Also:

Wikipedia: Quantile function

density

public double density(double x)

Description copied from interface: ProbabilityDistribution

The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space. \[ f(x) = dF(X) / dx \] This may not always exist.

For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.

Specified by:

density in interface ProbabilityDistribution

Parameters:

x - x

Returns:

f(x)

See Also:

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

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