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A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

A p-variate multivariate normal distribution (also called a multinormal distribution) is a generalization of the bivariate normal distribution. The p-multivariate ...

If Y_i have normal independent distributions with mean 0 and variance 1, then chi^2=sum_(i=1)^rY_i^2 (1) is distributed as chi^2 with r degrees of freedom. This makes a chi^2 ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

A multivariate normal distribution in three variables. It has probability density function (1) where (2) The standardized trivariate normal distribution takes unit variances ...

A joint distribution function is a distribution function D(x,y) in two variables defined by D(x,y) = P(X<=x,Y<=y) (1) D_x(x) = lim_(y->infty)D(x,y) (2) D_y(y) = ...

A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by (1) where Gamma(z) is the gamma function and _1F_1(a;b;z) is a ...

A standard normal distribution is a normal distribution with zero mean (mu=0) and unit variance (sigma^2=1), given by the probability density function and distribution ...

A distribution which arises in the study of integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)-1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)-1) = ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...