public class LogNormalDistribution extends AbstractRealDistribution
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.
| Modifier and Type | Field and Description |
|---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
|
randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY| Constructor and 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 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.
|
| Modifier and Type | Method and 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 |
cumulativeProbability(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 |
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()
Use this method to get information about whether the lower bound
of the support is inclusive or not.
|
boolean |
isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound
of the support is inclusive or not.
|
double |
probability(double x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X = x). |
double |
sample()
Generate a random value sampled from this distribution.
|
inverseCumulativeProbability, reseedRandomGenerator, samplepublic static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
public LogNormalDistribution(double scale,
double shape)
throws NotStrictlyPositiveException
scale - the scale parameter of this distributionshape - the shape parameter of this distributionNotStrictlyPositiveException - if shape <= 0.public LogNormalDistribution(double scale,
double shape,
double inverseCumAccuracy)
throws NotStrictlyPositiveException
scale - the scale parameter of this distributionshape - the shape parameter of this distributioninverseCumAccuracy - Inverse cumulative probability accuracy.NotStrictlyPositiveException - if shape <= 0.public LogNormalDistribution()
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.public double getScale()
public double getShape()
public double probability(double x)
X whose values are distributed according
to this distribution, this method returns P(X = x). In other
words, this method represents the probability mass function (PMF)
for the distribution.
For this distribution P(X = x) always evaluates to 0.x - the point at which the PMF is evaluatedpublic double density(double x)
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.x - the point at which the PDF is evaluatedxpublic double cumulativeProbability(double x)
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.x - the point at which the CDF is evaluatedxpublic double cumulativeProbability(double x0,
double x1)
throws NumberIsTooLargeException
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)
cumulativeProbability in interface RealDistributioncumulativeProbability in class AbstractRealDistributionx0 - the exclusive lower boundx1 - the inclusive upper boundx0 and x1,
excluding the lower and including the upper endpointNumberIsTooLargeException - if x0 > x1protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy in class AbstractRealDistributionpublic double getNumericalMean()
m and shape s, the mean is
exp(m + s^2 / 2).Double.NaN if it is not definedpublic double getNumericalVariance()
m and shape s, the variance is
(exp(s^2) - 1) * exp(2 * m + s^2).Double.POSITIVE_INFINITY as
for certain cases in TDistribution) or Double.NaN if it
is not definedpublic double getSupportLowerBound()
inverseCumulativeProbability(0). In other words, this
method must return
inf {x in R | P(X <= x) > 0}.
public double getSupportUpperBound()
inverseCumulativeProbability(1). In other words, this
method must return
inf {x in R | P(X <= x) = 1}.
Double.POSITIVE_INFINITY)public boolean isSupportLowerBoundInclusive()
public boolean isSupportUpperBoundInclusive()
public boolean isSupportConnected()
truepublic double sample()
sample in interface RealDistributionsample in class AbstractRealDistributionCopyright © 2003-2012 The Apache Software Foundation. All Rights Reserved.