Interface Distribution
 All Superinterfaces:
Serializable
 All Known Subinterfaces:
ExponentialFamily
 All Known Implementing Classes:
BernoulliDistribution
,BetaDistribution
,BinomialDistribution
,ChiSquareDistribution
,DiscreteDistribution
,DiscreteExponentialFamilyMixture
,DiscreteMixture
,EmpiricalDistribution
,ExponentialDistribution
,ExponentialFamilyMixture
,FDistribution
,GammaDistribution
,GaussianDistribution
,GaussianMixture
,GeometricDistribution
,HyperGeometricDistribution
,KernelDensity
,LogisticDistribution
,LogNormalDistribution
,Mixture
,NegativeBinomialDistribution
,PoissonDistribution
,ShiftedGeometricDistribution
,TDistribution
,WeibullDistribution
Both rejection and inverse transform sampling methods are implemented to provide some general approaches to generate random samples based on probability density function or quantile function. Besides, a quantile function is also provided based on bisection searching.
 See Also:

Method Summary
Modifier and TypeMethodDescriptiondouble
cdf
(double x) Cumulative distribution function.double
entropy()
Returns Shannon entropy of the distribution.default double
Use inverse transform sampling (also known as the inverse probability integral transform or inverse transformation method or Smirnov transform) to draw a sample from the given distribution.int
length()
Returns the number of parameters of the distribution.default double
likelihood
(double[] x) The likelihood of the sample set following this distribution.default double
logLikelihood
(double[] x) The log likelihood of the sample set following this distribution.double
logp
(double x) The density at x in log scale, which may prevents the underflow problem.double
mean()
Returns the mean of distribution.double
p
(double x) The probability density function for continuous distribution or probability mass function for discrete distribution at x.double
quantile
(double p) The quantile, the probability to the left of quantile is p.default double
quantile
(double p, double xmin, double xmax) Inversion of CDF by bisection numeric root finding of "cdf(x) = p" for continuous distribution.default double
quantile
(double p, double xmin, double xmax, double eps) Inversion of CDF by bisection numeric root finding of "cdf(x) = p" for continuous distribution.double
rand()
Generates a random number following this distribution.default double[]
rand
(int n) Generates a set of random numbers following this distribution.default double
rejectionSampling
(double pmax, double xmin, double xmax) Use the rejection technique to draw a sample from the given distribution.default double
sd()
Returns the standard deviation of distribution.double
variance()
Returns the variance of distribution.

Method Details

length
int length()Returns the number of parameters of the distribution. The "length" is in the sense of the minimum description length principle. Returns:
 The number of parameters.

mean
double mean()Returns the mean of distribution. Returns:
 The mean.

variance
double variance()Returns the variance of distribution. Returns:
 The variance.

sd
default double sd()Returns the standard deviation of distribution. Returns:
 The standard deviation.

entropy
double entropy()Returns Shannon entropy of the distribution. Returns:
 Shannon entropy.

rand
double rand()Generates a random number following this distribution. Returns:
 a random number.

rand
default double[] rand(int n) Generates a set of random numbers following this distribution. Parameters:
n
 the number of random numbers to generate. Returns:
 an array of random numbers.

p
double p(double x) The probability density function for continuous distribution or probability mass function for discrete distribution at x. Parameters:
x
 a real number. Returns:
 the density.

logp
double logp(double x) The density at x in log scale, which may prevents the underflow problem. Parameters:
x
 a real number. Returns:
 the log density.

cdf
double cdf(double x) Cumulative distribution function. That is the probability to the left of x. Parameters:
x
 a real number. Returns:
 the probability.

quantile
double quantile(double p) The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf. Parameters:
p
 the probability. Returns:
 the quantile.

likelihood
default double likelihood(double[] x) The likelihood of the sample set following this distribution. Parameters:
x
 a set of samples. Returns:
 the likelihood.

logLikelihood
default double logLikelihood(double[] x) The log likelihood of the sample set following this distribution. Parameters:
x
 a set of samples. Returns:
 the log likelihood.

rejectionSampling
default double rejectionSampling(double pmax, double xmin, double xmax) Use the rejection technique to draw a sample from the given distribution. WARNING: this simulation technique can take a very long time. Rejection sampling is also commonly called the acceptancerejection method or "acceptreject algorithm". It generates sampling values from an arbitrary probability distribution function f(x) by using an instrumental distribution g(x), under the only restriction thatf(x) < M g(x)
whereM > 1
is an appropriate bound onf(x) / g(x)
.Rejection sampling is usually used in cases where the form of
f(x)
makes sampling difficult. Instead of sampling directly from the distributionf(x)
, we use an envelope distributionM g(x)
where sampling is easier. These samples fromM g(x)
are probabilistically accepted or rejected.This method relates to the general field of Monte Carlo techniques, including Markov chain Monte Carlo algorithms that also use a proxy distribution to achieve simulation from the target distribution
f(x)
. It forms the basis for algorithms such as the Metropolis algorithm. Parameters:
pmax
 the scale of instrumental distribution (uniform).xmin
 the lower bound of random variable range.xmax
 the upper bound of random variable range. Returns:
 a random number.

inverseTransformSampling
default double inverseTransformSampling()Use inverse transform sampling (also known as the inverse probability integral transform or inverse transformation method or Smirnov transform) to draw a sample from the given distribution. This is a method for generating sample numbers at random from any probability distribution given its cumulative distribution function (cdf). Subject to the restriction that the distribution is continuous, this method is generally applicable (and can be computationally efficient if the cdf can be analytically inverted), but may be too computationally expensive in practice for some probability distributions. The BoxMuller transform is an example of an algorithm which is less general but more computationally efficient. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on, given substantial research effort, e.g. the ziggurat algorithm and rejection sampling. Returns:
 a random number.

quantile
default double quantile(double p, double xmin, double xmax, double eps) Inversion of CDF by bisection numeric root finding of "cdf(x) = p" for continuous distribution. Parameters:
p
 the probability.xmin
 the lower bound of search range.xmax
 the upper bound of search range.eps
 the epsilon close to zero. Returns:
 the quantile.

quantile
default double quantile(double p, double xmin, double xmax) Inversion of CDF by bisection numeric root finding of "cdf(x) = p" for continuous distribution. The default epsilon is 1E6. Parameters:
p
 the probability.xmin
 the lower bound of search range.xmax
 the upper bound of search range. Returns:
 the quantile.
