Package org.hipparchus.distribution.continuous

Class LogNormalDistribution

java.lang.Object

org.hipparchus.distribution.continuous.AbstractRealDistribution

org.hipparchus.distribution.continuous.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)

• m is the location parameter: this is the mean of the normally distributed natural logarithm of this distribution,
• s is the shape parameter: this is the standard deviation of the normally distributed natural logarithm of this distribution.

See Also:

• Log-normal distribution (Wikipedia)
• Log Normal distribution (MathWorld)
• Serialized Form

Field Summary

Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution

DEFAULT_SOLVER_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

Constructor	Description
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 location, double shape)	Create a log-normal distribution using the specified location and shape.
LogNormalDistribution(double location, double shape, double inverseCumAccuracy)	Creates a log-normal distribution.

Method Summary

Modifier and Type	Method	Description
double	cumulativeProbability(double x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	density(double x)	Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getLocation()	Returns the location parameter of this distribution.
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	getShape()	Returns the shape parameter of this distribution.
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. whether all values between the lower and upper bound of the support are included in the support.
double	logDensity(double x)	Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
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).

Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution

getSolverAbsoluteAccuracy, inverseCumulativeProbability

Methods inherited from class java.lang.Object

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

Constructor Details

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 location of the returned distribution is 0, while its shape is 1.

LogNormalDistribution

public LogNormalDistribution(double location,
 double shape)
                      throws MathIllegalArgumentException

Create a log-normal distribution using the specified location and shape.

Parameters:

location - the location parameter of this distribution

shape - the shape parameter of this distribution

Throws:

MathIllegalArgumentException - if shape <= 0.

LogNormalDistribution

public LogNormalDistribution(double location,
 double shape,
 double inverseCumAccuracy)
                      throws MathIllegalArgumentException

Creates a log-normal distribution.

Parameters:

location - Location parameter of this distribution.

shape - Shape parameter of this distribution.

inverseCumAccuracy - Inverse cumulative probability accuracy.

Throws:

MathIllegalArgumentException - if shape <= 0.

Method Details

getLocation

public double getLocation()

Returns the location parameter of this distribution.

Returns:

the location parameter

Since:

1.4

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 location m, and shape s of this distribution, the PDF is given by

• 0 if x <= 0,
• exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x) otherwise.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

logDensity

public double logDensity(double x)

Returns the natural logarithm of 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double).

The default implementation simply computes the logarithm of density(x). See documentation of density(double) for computation details.

Specified by:

logDensity in interface RealDistribution

Overrides:

logDensity in class AbstractRealDistribution

Parameters:

x - the point at which the PDF is evaluated

Returns:

the logarithm of 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 location m, and shape s of this distribution, the CDF is given by

• 0 if x <= 0,
• 0 if ln(x) - m < 0 and m - ln(x) > 40 * s, as in these cases the actual value is within Double.MIN_VALUE of 0,
• 1 if ln(x) - m >= 0 and ln(x) - m > 40 * s, as in these cases the actual value is within Double.MIN_VALUE of 1,
• 0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2)) otherwise.

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

probability

public double probability(double x0,
 double x1)
                   throws MathIllegalArgumentException

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

Specified by:

probability in interface RealDistribution

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:

MathIllegalArgumentException - if x0 > x1. The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For location 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 location 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)

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