
Bravais Distribution
< Back to Probability Distribution List The Bravais distribution is another name for the bivariate normal distribution, (also sometimes called the bivariate Gaussian or Bivariate Laplace–Gauss distribution). Teugels & Sundt lists the Bravais distribution as the probability density function of the bivariate normal random vector, X = X1, X2)T which is Haight published a simple […]

Beta Distribution
< Back to Probability Distributions List The beta distribution (also called the beta distribution of the first kind) is a family of continuous probability distributions defined on [0, 1]. The beta distribution is similar to the binomial distribution, except where the binomial models the number of successes (x), the beta models the probability (p) of success. […]

Binomials Added Distribution
< Back to Probability Distributions List Haight [1] lists the “binomials added distribution” as a single entry without a formula: MR17 refers to Mathematical reviews, which Haight notes as “in no case offer a review of a paper appearing in coded journals” and indicating “…publications in obscure (from the point of view of [1951]) sources.” […]

Student’s T Distribution
< Back to Probability Distribution List Student’s TDistribution (sometimes called the Student Distribution or TDistribution) is a family of probability distributions that are similar in shape to the normal distribution. Student’s tdistribution is used instead of the normal distribution when you have small samples or don’t know the population standard deviation. In real life, you usually […]

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 […]