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The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

Bayesian analysis is a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution. Begin with a "prior ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

A variable x is memoryless with respect to t if, for all s with t!=0, P(x>s+t|x>t)=P(x>s). (1) Equivalently, (P(x>s+t,x>t))/(P(x>t)) = P(x>s) (2) P(x>s+t) = P(x>s)P(x>t). (3) ...

Probability and Statistics

The ratio of two independent estimates of the variance of a normal distribution.

Involving two variables, as opposed to many (multivariate), or one (univariate).

A function that joins univariate distribution functions to form multivariate distribution functions. A two-dimensional copula is a function C:I^2->I such that C(0,t)=C(t,0)=0 ...

Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that H(x,y)=C(F(x),G(y)). Conversely, for any ...