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A statistical distribution in which the variates occur with probabilities asymptotically matching their "true" underlying statistical distribution is said to be random.

Let a set of random variates X_1, X_2, ..., X_n have a probability function P(X_1=x_1,...,X_n=x_n)=(N!)/(product_(i=1)^(n)x_i!)product_(i=1)^ntheta_i^(x_i) (1) where x_i are ...

The Laplace distribution, also called the double exponential distribution, is the distribution of differences between two independent variates with identical exponential ...

Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

The ratio X/Y of independent normally distributed variates with zero mean is distributed with a Cauchy distribution. This can be seen as follows. Let X and Y both have mean 0 ...

The distribution with probability density function and distribution function P(r) = (re^(-r^2/(2s^2)))/(s^2) (1) D(r) = 1-e^(-r^2/(2s^2)) (2) for r in [0,infty) and parameter ...

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2) where delta(x) ...

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 ...