
Arfwedson Distribution
< Back to Probability Distribution List The Arfwedson distribution is a discrete probability distribution for an urn sampling problem for drawings without replacement. Specifically, it tackles the problem “An urn contains N numbered balls. We make n drawings replacing the ball into the urn each time. What is the probability of getting v different balls?” […]

Rutherford’s Contagious Distribution
< Back to Probability Distribution List Rutherford’s contagious distribution (or simply the Rutherford distribution) was inspired by the Pólya urn model, from which it arises naturally [1]. The distribution, built on prior work by Woodbury [2] concerns the probability of a success at any trial which depends linearly on the number of previous successes. Woodbury […]

SemiNormal Distribution
< Back to Probability Distribution List According to Haight (1958), the “SemiNormal distribution” is another name for the Helmert Distribution [1], which is itself another name for the chisquare distribution. The name “seminormal” was coined by Steffensen [2] in a 1937 article titled “On the seminormal distribution” which appeared in volume 20 of Skandinavisk Aktuarietidskrift. […]

SemiTriangular Distribution
< Back to Probability Distribution List Haight’s 1958 Index to the Distributions of Mathematical Statistics [1] lists the following formula for the semitriangular distribution (p. 106): For 0 ≤ x ≤a [2]. With grouping corrections. The formula originated from an article by Kupperman in an article titled On Exact Grouping Corrections to Moments and Cumulants (pp. […]

Two Rectangulars Added Distribution
< Back to Probability Distribution List The “Two rectangulars added distribution” seems to be lost to history, although it is likely connected to the IrwinHall distribution. History of Two Rectangulars Added Distribution The entry for “two rectangulars Added” in Haight’s 1958 Index to the Distributions of Mathematical Statistics [1] refers to two rectangular distributions added […]

Power Function Distribution
< Back to Probability Distribution List The power function distribution (PFD) is a flexible model used to analyze and model income distribution data, lifetime data, and modeling of failure processes. One strength of the power function distribution is its mathematical simplicity, compared to more complex distributions like the Weibull distribution. The power function distribution is a special case […]

Generalized Inverse Normal Distribution
< Back to Probability Distribution List The term “inverse normal distribution” is informal and doesn’t refer to a specific probability distribution [1]. However, there is an inverse normal density function in statistics that reverses the procedure for finding zvalues (see “Inverse Normal Distribution” below). There is a generalized inverse normal distribution family, proposed by Robert […]

Asymptotic Normal Distribution
< Back to Probability Distribution List An asymptotic normal distribution is one that exhibits a property called asymptotic normality. Asymptotic normality is a property of an estimator (like the sample mean or sample standard deviation). The term “Asymptotic” refers to how the estimator behaves as the sample size tends to infinity; an estimator that has […]

LogNormal Distribution
< Back to Probability Distribution List The random variables that make up the lognormal distribution have normally distributed logarithms. As Y = ln(x) only exists for positive values of x, lognormal distributions have allpositive values. The lognormal distribution is particularly suited to fit skewed data with low mean and large variance. This occurs frequently in real life, […]

Mixture distribution
< Back to Probability Distributions List A mixture distribution is a distribution with two or more combined probability distributions; A new distribution is created by drawing random variables from two or more parent. The parent populations can be univariate distributions or multivariate distributions. The mixture distributions should be comprised of distributions with the same dimension. […]