# 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 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
getSupportLowerBound()
Access the lower bound of the support.
double
getSupportUpperBound()
Access the upper bound of the support.
double
inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
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).
• ## Method Details

• ### probability

double probability(double x0, double x1) throws MathIllegalArgumentException
For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
Parameters:
x0 - the exclusive lower bound
x1 - the inclusive upper bound
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
Throws:
MathIllegalArgumentException - if x0 > x1
• ### density

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.
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 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. 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 density(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 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.
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

double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
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.
Parameters:
p - the cumulative probability
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
Throws:
MathIllegalArgumentException - if p < 0 or p > 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 in TDistribution) or Double.NaN if it is not defined
• ### getSupportLowerBound

double getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {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 as inverseCumulativeProbability(1). In other words, this method must return

inf {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