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.
|
random, 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.
|
LogNormalDistribution(RandomGenerator rng,
double scale,
double shape)
Creates a log-normal distribution.
|
LogNormalDistribution(RandomGenerator rng,
double scale,
double shape,
double inverseCumAccuracy)
Creates a log-normal distribution.
|
| 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)
Deprecated.
|
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 |
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). |
double |
sample()
Generate a random value sampled from this distribution.
|
inverseCumulativeProbability, probability, reseedRandomGenerator, samplepublic static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
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.
Note: this constructor will implicitly create an instance of
Well19937c as random generator to be used for sampling only (see
sample() and AbstractRealDistribution.sample(int)). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
public LogNormalDistribution(double scale,
double shape)
throws NotStrictlyPositiveException
Note: this constructor will implicitly create an instance of
Well19937c as random generator to be used for sampling only (see
sample() and AbstractRealDistribution.sample(int)). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
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
Note: this constructor will implicitly create an instance of
Well19937c as random generator to be used for sampling only (see
sample() and AbstractRealDistribution.sample(int)). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
scale - the scale parameter of this distributionshape - the shape parameter of this distributioninverseCumAccuracy - Inverse cumulative probability accuracy.NotStrictlyPositiveException - if shape <= 0.public LogNormalDistribution(RandomGenerator rng, double scale, double shape) throws NotStrictlyPositiveException
rng - Random number generator.scale - Scale parameter of this distribution.shape - Shape parameter of this distribution.NotStrictlyPositiveException - if shape <= 0.public LogNormalDistribution(RandomGenerator rng, double scale, double shape, double inverseCumAccuracy) throws NotStrictlyPositiveException
rng - Random number generator.scale - Scale parameter of this distribution.shape - Shape parameter of this distribution.inverseCumAccuracy - Inverse cumulative probability accuracy.NotStrictlyPositiveException - if shape <= 0.public double getScale()
public double getShape()
public 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 logDensity(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. 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.logDensity in class AbstractRealDistributionx - 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 evaluatedx@Deprecated public double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException
RealDistribution.cumulativeProbability(double,double)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 > x1public double probability(double x0,
double x1)
throws NumberIsTooLargeException
X whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1).probability in class AbstractRealDistributionx0 - Lower bound (excluded).x1 - Upper bound (included).x0 and x1, excluding the lower
and including the upper endpoint.NumberIsTooLargeException - if x0 > x1.
The default implementation uses the identity
P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)protected 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()
getSupporLowerBound() is finite and
density(getSupportLowerBound()) returns a non-NaN, non-infinite
value.public boolean isSupportUpperBoundInclusive()
getSupportUpperBound() is finite and
density(getSupportUpperBound()) returns a non-NaN, non-infinite
value.public boolean isSupportConnected()
truepublic double sample()
sample in interface RealDistributionsample in class AbstractRealDistributionCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.