org.apache.commons.math3.distribution
Class LogNormalDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.AbstractRealDistribution
      extended by org.apache.commons.math3.distribution.LogNormalDistribution
All Implemented Interfaces:
Serializable, RealDistribution

public class LogNormalDistribution
extends AbstractRealDistribution

Implementation of the log-normal (gaussian) distribution.

Parameters: X is log-normally distributed if its natural logarithm log(X) is normally distributed. The probability distribution function of X is given by (for x > 0)

exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)

Since:
3.0
Version:
$Id: LogNormalDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $
See Also:
Log-normal distribution (Wikipedia), Log Normal distribution (MathWorld), Serialized Form

Field Summary
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
          Default inverse cumulative probability accuracy.
 
Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
 
Constructor Summary
LogNormalDistribution()
          Create a log-normal distribution, where the mean and standard deviation of the normally distributed natural logarithm of the log-normal distribution are equal to zero and one respectively.
LogNormalDistribution(double scale, double shape)
          Create a log-normal distribution using the specified scale and shape.
LogNormalDistribution(double scale, double shape, double inverseCumAccuracy)
          Create a log-normal distribution using the specified scale, shape and inverse cumulative distribution accuracy.
LogNormalDistribution(RandomGenerator rng, double scale, double shape, double inverseCumAccuracy)
          Creates a log-normal distribution.
 
Method Summary
 double cumulativeProbability(double x)
          For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
 double cumulativeProbability(double x0, double x1)
          Deprecated. See RealDistribution.cumulativeProbability(double,double)
 double density(double x)
          Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
 double getNumericalMean()
          Use this method to get the numerical value of the mean of this distribution.
 double getNumericalVariance()
          Use this method to get the numerical value of the variance of this distribution.
 double getScale()
          Returns the scale parameter of this distribution.
 double getShape()
          Returns the shape parameter of this distribution.
protected  double getSolverAbsoluteAccuracy()
          Returns the solver absolute accuracy for inverse cumulative computation.
 double getSupportLowerBound()
          Access the lower bound of the support.
 double getSupportUpperBound()
          Access the upper bound of the support.
 boolean isSupportConnected()
          Use this method to get information about whether the support is connected, i.e.
 boolean isSupportLowerBoundInclusive()
          Whether or not the lower bound of support is in the domain of the density function.
 boolean isSupportUpperBoundInclusive()
          Whether or not the upper bound of support is in the domain of the density function.
 double probability(double x0, double x1)
          For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
 double sample()
          Generate a random value sampled from this distribution.
 
Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
inverseCumulativeProbability, probability, reseedRandomGenerator, sample
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.

See Also:
Constant Field Values
Constructor Detail

LogNormalDistribution

public LogNormalDistribution()
Create a log-normal distribution, where the mean and standard deviation of the normally distributed natural logarithm of the log-normal distribution are equal to zero and one respectively. In other words, the scale of the returned distribution is 0, while its shape is 1.


LogNormalDistribution

public LogNormalDistribution(double scale,
                             double shape)
                      throws NotStrictlyPositiveException
Create a log-normal distribution using the specified scale and shape.

Parameters:
scale - the scale parameter of this distribution
shape - the shape parameter of this distribution
Throws:
NotStrictlyPositiveException - if shape <= 0.

LogNormalDistribution

public LogNormalDistribution(double scale,
                             double shape,
                             double inverseCumAccuracy)
                      throws NotStrictlyPositiveException
Create a log-normal distribution using the specified scale, shape and inverse cumulative distribution accuracy.

Parameters:
scale - the scale parameter of this distribution
shape - the shape parameter of this distribution
inverseCumAccuracy - Inverse cumulative probability accuracy.
Throws:
NotStrictlyPositiveException - if shape <= 0.

LogNormalDistribution

public LogNormalDistribution(RandomGenerator rng,
                             double scale,
                             double shape,
                             double inverseCumAccuracy)
                      throws NotStrictlyPositiveException
Creates a log-normal distribution.

Parameters:
rng - Random number generator.
scale - Scale parameter of this distribution.
shape - Shape parameter of this distribution.
inverseCumAccuracy - Inverse cumulative probability accuracy.
Throws:
NotStrictlyPositiveException - if shape <= 0.
Since:
3.1
Method Detail

getScale

public double getScale()
Returns the scale parameter of this distribution.

Returns:
the scale parameter

getShape

public double getShape()
Returns the shape parameter of this distribution.

Returns:
the shape parameter

density

public double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient. For scale m, and shape s of this distribution, the PDF is given by

Parameters:
x - the point at which the PDF is evaluated
Returns:
the value of the probability density function at point x

cumulativeProbability

public double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. For scale m, and shape s of this distribution, the CDF is given by

Parameters:
x - the point at which the CDF is evaluated
Returns:
the probability that a random variable with this distribution takes a value less than or equal to x

cumulativeProbability

@Deprecated
public double cumulativeProbability(double x0,
                                               double x1)
                             throws NumberIsTooLargeException
Deprecated. See RealDistribution.cumulativeProbability(double,double)

For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1). The default implementation uses the identity

P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

Specified by:
cumulativeProbability in interface RealDistribution
Overrides:
cumulativeProbability in class AbstractRealDistribution
Parameters:
x0 - the exclusive lower bound
x1 - the inclusive upper bound
Returns:
the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint
Throws:
NumberIsTooLargeException - if x0 > x1

probability

public double probability(double x0,
                          double x1)
                   throws NumberIsTooLargeException
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).

Overrides:
probability in class AbstractRealDistribution
Parameters:
x0 - Lower bound (excluded).
x1 - Upper bound (included).
Returns:
the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.
Throws:
NumberIsTooLargeException - if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:
getSolverAbsoluteAccuracy in class AbstractRealDistribution
Returns:
the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution. For scale m and shape s, the mean is exp(m + s^2 / 2).

Returns:
the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution. For scale m and shape s, the variance is (exp(s^2) - 1) * exp(2 * m + s^2).

Returns:
the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the parameters.

Returns:
lower bound of the support (always 0)

getSupportUpperBound

public double getSupportUpperBound()
Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()
Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:
true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:
true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:
true

sample

public double sample()
Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Specified by:
sample in interface RealDistribution
Overrides:
sample in class AbstractRealDistribution
Returns:
a random value.


Copyright © 2003-2012 The Apache Software Foundation. All Rights Reserved.