Package org.hipparchus.distribution
Interface RealDistribution
 All Known Implementing Classes:
AbstractRealDistribution
,BetaDistribution
,CauchyDistribution
,ChiSquaredDistribution
,ConstantRealDistribution
,EmpiricalDistribution
,EnumeratedRealDistribution
,ExponentialDistribution
,FDistribution
,GammaDistribution
,GumbelDistribution
,LaplaceDistribution
,LevyDistribution
,LogisticDistribution
,LogNormalDistribution
,NakagamiDistribution
,NormalDistribution
,ParetoDistribution
,TDistribution
,TriangularDistribution
,UniformRealDistribution
,WeibullDistribution
public interface RealDistribution
Base interface for continuous distributions.

Method Summary
Modifier and TypeMethodDescriptiondouble
cumulativeProbability
(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
density
(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.double
Access the lower bound of the support.double
Access the upper bound of the support.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.boolean
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 pointx
.double
probability
(double x0, double x1) For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.

Method Details

probability
For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
. Parameters:
x0
 the exclusive lower boundx1
 the inclusive upper bound Returns:
 the probability that a random variable with this distribution
takes a value between
x0
andx1
, excluding the lower and including the upper endpoint  Throws:
MathIllegalArgumentException
 ifx0 > x1

density
double density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. If the derivative does not exist atx
, 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. Parameters:
x
 the point at which the PDF is evaluated Returns:
 the value of the probability density function at point
x

logDensity
double logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. If the derivative does not exist atx
, 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 ofdensity(double)
. 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
double cumulativeProbability(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. 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

inverseCumulativeProbability
Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value isinf{x in R  P(X<=x) >= p}
for0 < p <= 1
,inf{x in R  P(X<=x) > 0}
forp = 0
.
 Parameters:
p
 the cumulative probability Returns:
 the smallest
p
quantile of this distribution (largest 0quantile forp = 0
)  Throws:
MathIllegalArgumentException
 ifp < 0
orp > 1

getNumericalMean
double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. Returns:
 the mean or
Double.NaN
if it is not defined

getNumericalVariance
double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. Returns:
 the variance (possibly
Double.POSITIVE_INFINITY
as for certain cases inTDistribution
) orDouble.NaN
if it is not defined

getSupportLowerBound
double getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must returninf {x in R  P(X <= x) > 0}
. Returns:
 lower bound of the support (might be
Double.NEGATIVE_INFINITY
)

getSupportUpperBound
double getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must returninf {x in R  P(X <= x) = 1}
. Returns:
 upper bound of the support (might be
Double.POSITIVE_INFINITY
)

isSupportConnected
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. Returns:
 whether the support is connected or not
