Serializable
, RealDistribution
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.
DEFAULT_SOLVER_ABSOLUTE_ACCURACY
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 scale,
double shape) |
Create a log-normal distribution using the specified scale and shape.
|
LogNormalDistribution(double scale,
double shape,
double inverseCumAccuracy) |
Creates a log-normal distribution.
|
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 |
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.
|
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.
|
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) . |
getSolverAbsoluteAccuracy, inverseCumulativeProbability
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 LogNormalDistribution(double scale, double shape) throws MathIllegalArgumentException
scale
- the scale parameter of this distributionshape
- the shape parameter of this distributionMathIllegalArgumentException
- if shape <= 0
.public LogNormalDistribution(double scale, double shape, double inverseCumAccuracy) throws MathIllegalArgumentException
scale
- Scale parameter of this distribution.shape
- Shape parameter of this distribution.inverseCumAccuracy
- Inverse cumulative probability accuracy.MathIllegalArgumentException
- 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 evaluatedx
public 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 interface RealDistribution
logDensity
in class AbstractRealDistribution
x
- the point at which the PDF is evaluatedx
public 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
public double probability(double x0, double x1) throws MathIllegalArgumentException
X
whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1)
.probability
in interface RealDistribution
probability
in class AbstractRealDistribution
x0
- Lower bound (excluded).x1
- Upper bound (included).x0
and x1
, excluding the lower
and including the upper endpoint.MathIllegalArgumentException
- if x0 > x1
.
The default implementation uses the identity
P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
public 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 isSupportConnected()
true
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