LogNormalDistribution (VirtualDataSet API)

java.lang.Object
- org.apache.commons.statistics.distribution.LogNormalDistribution

All Implemented Interfaces:

ContinuousDistribution
```
public class LogNormalDistribution
extends java.lang.Object
```
Implementation of the log-normal 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 scale 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.

Nested Class Summary
- Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
  ContinuousDistribution.Sampler

Constructor Summary

Constructors
Constructor Description

LogNormalDistribution(double scale, double shape)
Creates a log-normal distribution.

Constructors
Constructor	Description
`LogNormalDistribution(double scale, double shape)`	Creates a log-normal distribution.

Method Summary

Modifier and Type	Method	Description
`ContinuousDistribution.Sampler`	`createSampler(UniformRandomProvider rng)`	Creates a sampler.
`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`	`getMean()`	Gets the mean of this distribution.
`double`	`getScale()`	Returns the scale parameter of this distribution.
`double`	`getShape()`	Returns the shape parameter of this distribution.
`double`	`getSupportLowerBound()`	Gets the lower bound of the support.
`double`	`getSupportUpperBound()`	Gets the upper bound of the support.
`double`	`getVariance()`	Gets the variance of this distribution.
`double`	`inverseCumulativeProbability(double p)`	Computes the quantile function of this distribution.
`boolean`	`isSupportConnected()`	Indicates whether the support is connected, i.e.
`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)`.
`static double[]`	`sample(int n, ContinuousDistribution.Sampler sampler)`	Utility function for allocating an array and filling it with `n` samples generated by the given `sampler`.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
probability

- Constructor Detail
  - LogNormalDistribution
```
public LogNormalDistribution(double scale,
                             double shape)
```
    Creates a log-normal distribution.
    
    Parameters:
    
    scale - Scale parameter of this distribution.
    
    shape - Shape parameter of this distribution.
    
    Throws:
    
    java.lang.IllegalArgumentException - if shape <= 0.
- 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
    
    0 if x <= 0,
    
    exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x) otherwise.
    Parameters:
    
    x - Point at which the PDF is evaluated.
    
    Returns:
    
    the value of the probability density function at 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. See documentation of density(double) for computation details.
    
    Parameters:
    
    x - Point at which the PDF is evaluated.
    
    Returns:
    
    the logarithm of the value of the probability density function at 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
    
    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 - 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)
```
    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)
    
    Parameters:
    
    x0 - Lower bound (exclusive).
    
    x1 - Upper bound (inclusive).
    
    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.
  - getMean
```
public double getMean()
```
    Gets 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.
  - getVariance
```
public double getVariance()
```
    Gets 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, or Double.NaN if it is not defined.
  - getSupportLowerBound
```
public double getSupportLowerBound()
```
    Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. 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()
```
    Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. 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()
```
    Indicates 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
  - createSampler
```
public ContinuousDistribution.Sampler createSampler(UniformRandomProvider rng)
```
    Creates a sampler.
    
    Specified by:
    
    createSampler in interface ContinuousDistribution
    
    Parameters:
    
    rng - Generator of uniformly distributed numbers.
    
    Returns:
    
    a sampler that produces random numbers according this distribution.
  - inverseCumulativeProbability
```
public double inverseCumulativeProbability(double p)
```
    Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
    
    inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
    
    inf{x in R | P(X<=x) > 0} for p = 0.
    
    The default implementation returns
    
    ContinuousDistribution.getSupportLowerBound() for p = 0,
    
    ContinuousDistribution.getSupportUpperBound() for p = 1.
    Specified by:
    
    inverseCumulativeProbability in interface ContinuousDistribution
    
    Parameters:
    
    p - Cumulative probability.
    
    Returns:
    
    the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
  - sample
```
public static double[] sample(int n,
                              ContinuousDistribution.Sampler sampler)
```
    Utility function for allocating an array and filling it with n samples generated by the given sampler.
    
    Parameters:
    
    n - Number of samples.
    
    sampler - Sampler.
    
    Returns:
    
    an array of size n.

Class LogNormalDistribution

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

Constructor Detail

LogNormalDistribution

Method Detail

getScale

getShape

density

logDensity

cumulativeProbability

probability

getMean

getVariance

getSupportLowerBound

getSupportUpperBound

isSupportConnected

createSampler

inverseCumulativeProbability

sample