Package smile.stat.distribution

Probability distributions.

See: Description

Interface Summary

Interface	Description
DiscreteExponentialFamily	The purpose of this interface is mainly to define the method M that is the Maximization step in the EM algorithm.
Distribution	Probability distribution of univariate random variable.
ExponentialFamily	The exponential family is a class of probability distributions sharing a certain form.
MultivariateDistribution	Probability distribution of multivariate random variable.
MultivariateExponentialFamily	The purpose of this interface is mainly to define the method M that is the Maximization step in the EM algorithm.

Class Summary

Class	Description
AbstractDistribution	This is the base class of univariate distributions.
AbstractMultivariateDistribution	This is the base class of multivariate distributions.
BernoulliDistribution	Bernoulli distribution is a discrete probability distribution, which takes value 1 with success probability p and value 0 with failure probability q = 1 - p.
BetaDistribution	The beta distribution is defined on the interval [0, 1] parameterized by two positive shape parameters, typically denoted by α and β.
BIC	Bayesian information criterion (BIC) or Schwarz Criterion is a criterion for model selection among a class of parametric models with different numbers of parameters.
BinomialDistribution	The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.
ChiSquareDistribution	Chi-square (or chi-squared) distribution with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables.
DiscreteDistribution	This is the base class of univariate discrete distributions.
DiscreteExponentialFamilyMixture	The finite mixture of distributions from discrete exponential family.
DiscreteMixture	The finite mixture of discrete distributions.
DiscreteMixture.Component	A component in the mixture distribution is defined by a distribution and its weight in the mixture.
EmpiricalDistribution	An empirical distribution function or empirical cdf, is a cumulative probability distribution function that concentrates probability 1/n at each of the n numbers in a sample.
ExponentialDistribution	An exponential distribution describes the times between events in a Poisson process, in which events occur continuously and independently at a constant average rate.
ExponentialFamilyMixture	The finite mixture of distributions from exponential family.
FDistribution	F-distribution arises in the testing of whether two observed samples have the same variance.
GammaDistribution	The Gamma distribution is a continuous probability distributions with a scale parameter θ and a shape parameter k.
GaussianDistribution	The normal distribution or Gaussian distribution is a continuous probability distribution that describes data that clusters around a mean.
GaussianMixture	Finite univariate Gaussian mixture.
GeometricDistribution	The geometric distribution is a discrete probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set {1, 2, 3, …}.
HyperGeometricDistribution	The hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement, just as the binomial distribution describes the number of successes for draws with replacement.
KernelDensity	Kernel density estimation is a non-parametric way of estimating the probability density function of a random variable.
LogisticDistribution	The logistic distribution is a continuous probability distribution whose cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks.
LogNormalDistribution	A log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed.
Mixture	A finite mixture model is a probabilistic model for density estimation using a mixture distribution.
Mixture.Component	A component in the mixture distribution is defined by a distribution and its weight in the mixture.
MultivariateExponentialFamilyMixture	The finite mixture of distributions from multivariate exponential family.
MultivariateGaussianDistribution	Multivariate Gaussian distribution.
MultivariateGaussianMixture	Finite multivariate Gaussian mixture.
MultivariateMixture	The finite mixture of multivariate distributions.
MultivariateMixture.Component	A component in the mixture distribution is defined by a distribution and its weight in the mixture.
NegativeBinomialDistribution	Negative binomial distribution arises as the probability distribution of the number of successes in a series of independent and identically distributed Bernoulli trials needed to get a specified (non-random) number r of failures.
PoissonDistribution	Poisson distribution expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event.
ShiftedGeometricDistribution	The "shifted" geometric distribution is a discrete probability distribution of the number of failures before the first success, supported on the set {0, 1, 2, 3, …}.
TDistribution	Student's t-distribution (or simply the t-distribution) is a probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small.
WeibullDistribution	The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering.

Package smile.stat.distribution Description

Probability distributions. In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values.

In the discrete case, one can easily assign a probability to each possible value. In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals.

If total order is defined for the random variable, the cumulative distribution function gives the probability that the random variable is not larger than a given value; it is the integral of the non-cumulative distribution.

Author:

Haifeng Li