Seemingly unrelated regressions
In econometrics, the seemingly unrelated regressions or seemingly unrelated regression equations model, proposed by Arnold Zellner in, is a generalization of a linear regression model that consists of several regression equations, each having its ...
Probit
In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution, which is commonly denoted as N. Mathematically, it is the inverse of the cumulative distribution function of the ...
Atom (programming language)
Originally intended as a high level hardware description language, Atom was created in early 2007 and released in opensource of April of the same year. Inspired by TRS and Bluespec, Atom compiled circuit descriptions, that were based on guarded ...
Bhatia–Davis inequality
In mathematics, the Bhatia–Davis inequality, named after Rajendra Bhatia and Chandler Davis, is an upper bound on the variance σ 2 of any bounded probability distribution on the real line. Suppose a distribution has minimum m, maximum M, and expe ...
Cokurtosis
In probability theory and statistics, cokurtosis is a measure of how much two random variables change together. Cokurtosis is the fourth standardized cross central moment. If two random variables exhibit a high level of cokurtosis they will tend ...
Combinant
In the mathematical theory of probability, the combinants c n of a random variable X are defined via the combinantgenerating function G, which is defined from the moment generating function M as G X t = M X log 1 + t) {\displaystyle G_{X}t=M_{ ...
Comonotonicity
In probability theory, comonotonicity mainly refers to the perfect positive dependence between the components of a random vector, essentially saying that they can be represented as increasing functions of a single random variable. In two dimensio ...
Concomitant (statistics)
In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample. Let X i, Y i, i = 1., n be a random sample from ...
Conditional probability distribution
In probability theory and statistics, given two jointly distributed random variables X {\displaystyle X} and Y {\displaystyle Y}, the conditional probability distribution of Y given X is the probability distribution of Y {\displaystyle Y} when X ...
Convolution of probability distributions
The convolution of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear ...
Coskewness
In probability theory and statistics, coskewness is a measure of how much two random variables change together. Coskewness is the third standardized cross central moment, related to skewness as covariance is related to variance. In 1976, Krauss a ...
Hellinger distance
In probability and statistics, the Hellinger distance is used to quantify the similarity between two probability distributions. It is a type of f divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introdu ...
Infinite divisibility (probability)
In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables. The characteristic fun ...
Joint probability distribution
Given random variables X, Y, … {\displaystyle X,Y,\ldots }, that are defined on a probability space, the joint probability distribution for X, Y, … {\displaystyle X,Y,\ldots } is a probability distribution that gives the probability that each of ...
Khmaladze transformation
In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose X 1, …, X n {\displaystyle X_{1},\ldots,X_{n}} are i.i.d., p ...
Marginal distribution
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variable ...
Memorylessness
In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a "waiting time" until a certain event does not depend on how much time has elapsed already. ...
Mills ratio
In probability theory, the Mills ratio of a continuous random variable X {\displaystyle X} is the function m x:= F ¯ x f x, {\displaystyle mx:={\frac.}
Neutral vector
In statistics, and specifically in the study of the Dirichlet distribution, a neutral vector of random variables is one that exhibits a particular type of statistical independence amongst its elements. In particular, when elements of the random v ...
Normalizing constant
The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics. The normalizing constant is used to reduce any probability function to a probability density function with total probability of one.
Normally distributed and uncorrelated does not imply independent
In probability theory, although simple examples illustrate that linear uncorrelatedness of two random variables does not in general imply their independence, it is sometimes mistakenly thought that it does imply that when the two random variables ...
Pairwise independence
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise indepen ...
Popovicius inequality on variances
In probability theory, Popovicius inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ² of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particula ...
Probability integral transform
In statistics, the probability integral transform or transformation relates to the result that data values that are modelled as being random variables from any given continuous distribution can be converted to random variables having a standard u ...
Relationships among probability distributions
In probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following groups: Transforms function of a random variable; Duality; Approximation limit relationship ...
Shape of a probability distribution
In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population. The shape of a distr ...
Smoothness (probability theory)
In probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution’s characteristic function. Forma ...
Stability (probability)
In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. The distributions of random variables ha ...
Tail dependence
In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions. The concept is used in extreme value theory. Random variables that appear to exhibit no correlation can ...
Truncated distribution
In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases where the ability to record, or ...
Truncation (statistics)
In statistics, truncation results in values that are limited above or below, resulting in a truncated sample. A random variable y {\displaystyle y} is said to be truncated from below if, for some threshold value c {\displaystyle c}, the exact val ...
Zero bias transform
The zerobias transform is a transform from one probability distribution to another. The transform arises in applications of Steins method in probability and statistics.
Complex inverse Wishart distribution
The complex inverse Wishart distribution is a matrix probability distribution defined on complexvalued positivedefinite matrices and is the complex analog of the real inverse Wishart distribution. The complex Wishart distribution was extensivel ...
Compound probability distribution
In probability and statistics, a compound probability distribution is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with the parameters of that distribut ...
Beta prime distribution
In probability theory and statistics, the beta prime distribution is an absolutely continuous probability distribution defined for x > 0 {\displaystyle x> 0} with two parameters α and β, having the probability density function: f x = x α − ...
Beta rectangular distribution
In probability theory and statistics, the beta rectangular distribution is a probability distribution that is a finite mixture distribution of the beta distribution and the continuous uniform distribution. The support is of the distribution is in ...
Compound Poisson distribution
In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identicallydistributed random variables, where the number of terms to be added is itself a Poissondistributed variable. ...
Delaporte distribution
The Delaporte distribution is a discrete probability distribution that has received attention in actuarial science. It can be defined using the convolution of a negative binomial distribution with a Poisson distribution. Just as the negative bino ...
Exponentially modified Gaussian distribution
In probability theory, an exponentially modified Gaussian distribution describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Ga ...
Lomax distribution
The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavytail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lom ...
Normal variancemean mixture
In probability theory and statistics, a normal variancemean mixture with mixing probability density g {\displaystyle g} is the continuous probability distribution of a random variable Y {\displaystyle Y} of the form Y = α + β V + σ V X, {\displa ...
Rayleigh mixture distribution
In probability theory and statistics a Rayleigh mixture distribution is a weighted mixture of multiple probability distributions where the weightings are equal to the weightings of a Rayleigh distribution. Since the probability density function f ...
Yule–Simon distribution
In probability and statistics, the Yule–Simon distribution is a discrete probability distribution named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution. The probability mass function pmf of the Yule–Simon ρ ...
Bernoulli distribution
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p {\displaystyle p} and the ...
Generalized Dirichlet distribution
In statistics, the generalized Dirichlet distribution is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random variables with a GD distribution are not completely ...
Grouped Dirichlet distribution
In statistics, the grouped Dirichlet distribution is a multivariate generalization of the Dirichlet distribution It was first described by Ng et al 2008. The Grouped Dirichlet distribution arises in the analysis of categorical data where some obs ...
Inversegamma distribution
In probability theory and statistics, the inverse gamma distribution is a twoparameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to t ...
NormalinverseWishart distribution
In probability theory and statistics, the normalinverseWishart distribution is a multivariate fourparameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and c ...
NormalWishart distribution
In probability theory and statistics, the normalWishart distribution is a multivariate fourparameter family of continuous probability distributions. It is the conjugate prior of a multivariate normal distribution with unknown mean and precision ...
Arcsine distribution
In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function is F x = 2 π arcsin x = arcsin 2 x − 1 π + 1 2 {\displaystyle Fx={\frac {2}{\pi }}\arcsin \left{\sqrt {x}}\right={\frac {\a ...
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Asymmetric Laplace distribution 

Bates distribution 
Behrens–Fisher distribution 
Benini distribution 
Bingham distribution 
Birnbaum–Saunders distribution 

Bivariate von Mises distribution 

Burr distribution 
Champernowne distribution 

Chi distribution 

Circular uniform distribution 

Davis distribution 

Erlang distribution 

Exponentiallogarithmic distribution 
Exponentiated Weibull distribution 

Fdistribution 

Fishers zdistribution 

Frechet distribution 

Gamma/Gompertz distribution 
Generalised hyperbolic distribution 
Generalized chisquared distribution 
Generalized extreme value distribution 

Generalized gamma distribution 

Generalized inverse Gaussian distribu .. 
Generalized multivariate loggamma di .. 
Generalized normal distribution 
Linnik distribution 

Gumbel distribution 

Halflogistic distribution 

Halfnormal distribution 

Harmonic distribution 
Hotellings Tsquared distribution 

Hyperbolic distribution 

Hyperbolic secant distribution 

Hyperexponential distribution 
Hypoexponential distribution 

Inverse Gaussian distribution 

Inversechisquared distribution 

Irwin–Hall distribution 

Johnsons SUdistribution 

Kent distribution 

Kumaraswamy distribution 

LogCauchy distribution 

Loglogistic distribution 

Logitnormal distribution 
Marshall–Olkin exponential distribution 
McCullaghs parametrization of the Cau .. 
MittagLeffler distribution 
Moffat distribution 

Multimodal distribution 
Multivariate tdistribution 

Nakagami distribution 
Noncentral beta distribution 
Noncentral chi distribution 
Noncentral Fdistribution 

Noncentral tdistribution 
Normalinverse Gaussian distribution 

Normalinversegamma distribution 

PERT distribution 

Phasetype distribution 

Rayleigh distribution 

Reciprocal distribution 

Scaled inverse chisquared distribution 

Shifted Gompertz distribution 

Shifted loglogistic distribution 

Skew normal distribution 

Slash distribution 
Split normal distribution 

Studentized range distribution 
SubGaussian distribution 

Truncated normal distribution 

Tukey lambda distribution 

Uquadratic distribution 

Uniform distribution (continuous) 
Variancegamma distribution 

Von Mises distribution 
Von Mises–Fisher distribution 
Wakeby distribution 
Wilkss lambda distribution 

Wrapped asymmetric Laplace distribution 

Wrapped Cauchy distribution 

Wrapped exponential distribution 
Wrapped Levy distribution 

Wrapped normal distribution 

Bernoulli trial 
Borel distribution 
Categorical distribution 
Conway–Maxwell–binomial distribution 

Degenerate distribution 
Discrete phasetype distribution 

Discrete uniform distribution 
Discretestable distribution 

Fishers noncentral hypergeometric dis .. 

Geometric distribution 
Kirkwood approximation 

Logarithmic distribution 

Noncentral hypergeometric distributions 
Parabolic fractal distribution 
Rademacher distribution 

Skellam distribution 