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The triangle function is the function Lambda(x) = {0 |x|>=1; 1-|x| |x|<1 (1) = Pi(x)*Pi(x) (2) = Pi(x)*H(x+1/2)-Pi(x)*H(x-1/2), (3) where Pi(x) is the rectangle function, ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

The "kurtosis excess" (Kenney and Keeping 1951, p. 27) is defined in terms of the usual kurtosis by gamma_2 = beta_2-3 (1) = (mu_4)/(mu_2^2)-3. (2) It is commonly denoted ...

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 ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

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 ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...

Probability and Statistics