Probability distributions

In probability theory, a distribution is said to be stable (or a random variable is said to be stable) if a linear combination of two independent copies of a random sample has the same distribution, up to location and scale parameters.

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes in draws, without replacement, from a finite population of size that contains exactly successes, wherein each draw is either a success or a failure.

In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.

In probability theory and statistics, the binomial distribution with parameters n and p 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.

In probability theory and statistics, the Rayleigh distribution /ˈreɪli/ is a continuous probability distribution for positive-valued random variables.

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution.

In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance, e.

In probability theory and statistics, the Poisson distribution (French pronunciation [pwasɔ̃]; in English usually /ˈpwɑːsɒn/), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event.

In probability theory and statistics, the exponential distribution (a.k.a. negative exponential distribution) is the probability distribution that describes the time between events in a Poisson process, i.

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b.

Benford's law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power law probability distribution that is used in description of social, scientific, geophysical, actuarial, and many other types of observable phenomena.

Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate: It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto.

In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution, which is commonly denoted as N(0,1).

In statistics, the Davis distributions are a family of continuous probability distributions.

In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0 (analogous to an electronic rectifier).