de.lmu.ifi.dbs.elki.math.statistics.distribution

Class ExponentialDistribution

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.distribution.ExponentialDistribution

All Implemented Interfaces:

Distribution, DistributionWithRandom

public class ExponentialDistribution
extends Object
implements DistributionWithRandom

Exponential distribution.

Field Summary

Fields

Modifier and Type	Field and Description
(package private) double	rate Rate, inverse of mean
(package private) Random	rnd Random generator.

Constructor Summary

Constructors

Constructor and Description
ExponentialDistribution(double rate) Constructor.
ExponentialDistribution(double rate, Random random) Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
double	cdf(double val) Return the cumulative density function at the given value.
static double	cdf(double val, double rate) Cumulative density, static version
double	nextRandom() This method currently uses the naive approach of returning -log(uniform).
double	pdf(double val) Return the density of an existing value
static double	pdf(double val, double rate) PDF, static version
double	quantile(double val) Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double val, double rate) Quantile function, static version

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.lmu.ifi.dbs.elki.math.statistics.distribution.Distribution

toString

Field Detail

rnd

Random rnd

Random generator.

rate

double rate

Rate, inverse of mean

Constructor Detail

ExponentialDistribution

public ExponentialDistribution(double rate)

Constructor.

Parameters:

rate - Rate parameter (1/scale)

ExponentialDistribution

public ExponentialDistribution(double rate,
                       Random random)

Constructor.

Parameters:

rate - Rate parameter (1/scale)

random - Random generator

Method Detail

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Specified by:

pdf in interface Distribution

Parameters:

val - existing value

Returns:

distribution density

pdf

public static double pdf(double val,
         double rate)

PDF, static version

Parameters:

val - Value to compute PDF at

rate - Rate parameter (1/scale)

Returns:

probability density

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Specified by:

cdf in interface Distribution

Parameters:

val - existing value

Returns:

cumulative density

cdf

public static double cdf(double val,
         double rate)

Cumulative density, static version

Parameters:

val - Value to compute CDF at

rate - Rate parameter (1/scale)

Returns:

cumulative density

quantile

public double quantile(double val)

Description copied from interface: Distribution

Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.

Specified by:

quantile in interface Distribution

Parameters:

val - Quantile to find

Returns:

Quantile position

quantile

public static double quantile(double val,
              double rate)

Quantile function, static version

Parameters:

val - Value to compute quantile for

rate - Rate parameter

Returns:

Quantile

nextRandom

public double nextRandom()

This method currently uses the naive approach of returning -log(uniform). TODO: there are variants that do not rely on the log method and are faster. We need to implement and evaluate these. For details: see "Computer methods for sampling from the exponential and normal distributions" J. H. Ahrens, U. Dieter, https://dl.acm.org/citation.cfm?id=361593

Specified by:

nextRandom in interface DistributionWithRandom

Returns:

new random value