# 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
The base class of univariate 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.
The beta distribution is defined on the interval [0, 1] parameterized by two positive shape parameters, typically denoted by α and β.
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
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.
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.