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

Class LogNormalDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

@Alias(value="lognormal")
public class LogNormalDistribution
extends AbstractDistribution

Log-Normal distribution. The parameterization of this class is somewhere inbetween of GNU R and SciPy. Similar to GNU R we use the logmean and logstddev. Similar to Scipy, we also have a location parameter that shifts the distribution. Our implementation maps to SciPy's as follows: scipy.stats.lognorm(logstddev, shift, FastMath.exp(logmean))

Since:

0.5.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LogNormalDistribution.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and Description
private double	logmean Mean value for the generator
private double	logstddev Standard deviation
private double	shift Additional shift factor

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

random

Constructor Summary

Constructors

Constructor and Description
LogNormalDistribution(double logmean, double logstddev, double shift) Constructor.
LogNormalDistribution(double logmean, double logstddev, double shift, java.util.Random random) Constructor for Log-Normal distribution
LogNormalDistribution(double logmean, double logstddev, double shift, RandomFactory random) Constructor for Log-Normal distribution

Method Summary

Modifier and Type	Method and Description
double	cdf(double val) Return the cumulative density function at the given value.
static double	cdf(double x, double mu, double sigma) Cumulative probability density function (CDF) of a normal distribution.
double	getLogMean() Get the log mean value.
double	getLogStddev() Get the log standard deviation.
double	getShift() Get the distribution shift.
double	logpdf(double val) Return the log density of an existing value
static double	logpdf(double x, double mu, double sigma) Probability density function of the normal distribution.
double	nextRandom() Generate a new random value
double	pdf(double val) Return the density of an existing value
static double	pdf(double x, double mu, double sigma) Probability density function of the normal distribution.
double	quantile(double val) Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double x, double mu, double sigma) Inverse cumulative probability density function (probit) of a normal distribution.
java.lang.String	toString() Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

logmean

private double logmean

Mean value for the generator

logstddev

private double logstddev

Standard deviation

shift

private double shift

Additional shift factor

Constructor Detail

LogNormalDistribution

public LogNormalDistribution(double logmean,
                             double logstddev,
                             double shift,
                             java.util.Random random)

Constructor for Log-Normal distribution

Parameters:

logmean - Mean

logstddev - Standard Deviation

shift - Shifting offset

random - Random generator

LogNormalDistribution

public LogNormalDistribution(double logmean,
                             double logstddev,
                             double shift,
                             RandomFactory random)

Constructor for Log-Normal distribution

Parameters:

logmean - Mean

logstddev - Standard Deviation

shift - Shifting offset

random - Random generator

LogNormalDistribution

public LogNormalDistribution(double logmean,
                             double logstddev,
                             double shift)

Constructor.

Parameters:

logmean - Mean

logstddev - Standard deviation

shift - Shifting offset

Method Detail

getLogMean

public double getLogMean()

Get the log mean value.

Returns:

logmean

getLogStddev

public double getLogStddev()

Get the log standard deviation.

Returns:

log standard deviation

getShift

public double getShift()

Get the distribution shift.

Returns:

Shift

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Parameters:

val - existing value

Returns:

distribution density

logpdf

public double logpdf(double val)

Description copied from interface: Distribution

Return the log density of an existing value

Parameters:

val - existing value

Returns:

log distribution density

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Parameters:

val - existing value

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.

Parameters:

val - Quantile to find

Returns:

Quantile position

pdf

public static double pdf(double x,
                         double mu,
                         double sigma)

Probability density function of the normal distribution.

 1/(SQRT(2*pi)*sigma*x) * e^(-log(x-mu)^2/2sigma^2)
 

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

Returns:

PDF of the given normal distribution at x.

logpdf

public static double logpdf(double x,
                            double mu,
                            double sigma)

Probability density function of the normal distribution.

 1/(SQRT(2*pi)*sigma*x) * e^(-log(x-mu)^2/2sigma^2)
 

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

Returns:

logPDF of the given normal distribution at x.

cdf

public static double cdf(double x,
                         double mu,
                         double sigma)

Cumulative probability density function (CDF) of a normal distribution.

Parameters:

x - value to evaluate CDF at

mu - Mean value

sigma - Standard deviation.

Returns:

The CDF of the given normal distribution at x.

quantile

public static double quantile(double x,
                              double mu,
                              double sigma)

Inverse cumulative probability density function (probit) of a normal distribution.

Parameters:

x - value to evaluate probit function at

mu - Mean value

sigma - Standard deviation.

Returns:

The probit of the given normal distribution at x.

nextRandom

public double nextRandom()

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Overrides:

nextRandom in class AbstractDistribution

Returns:

new random value

toString

public java.lang.String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class java.lang.Object

Returns:

description