Probability distributions > Unusual Probability Distributions
These unusual probability distributions (or unusual names for distributions) never made it to the mainstream. You won’t find these in your regular textbooks, but I did come across this interesting list put together by Prof. Shakti .
List of Unusual Probability Distributions
- The array distribution refers to the conditional distribution of independent random variables X1 (given X2, … ,Xn).
- The Arfwedsen distribution (the coupon-collecting distribution or Dixie cup) 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?”
- Binomials Added Distribution: The problem of adding binomials was addressed briefly in , referencing a formula for a toric ideal. Otherwise, it seems to have disappeared into obscurity.
- Bipolar distribution: a specific type of bimodal distribution that has two distinct peaks offering contradictory information. In some cases, the term may also refer to the Watson bipolar distribution.
- The Bravais distribution is another name for the bivariate normal distribution, (also sometimes called the bivariate Gaussian or Bivariate Laplace–Gauss distribution).
- Chi-bar-squared distribution: a mixture of chi-square distributions, mixed over their degrees of freedom.
- Darmois-Koopman distribution (or Koopman-Darmois) is a member of the exponential-type class of probability distributions.
- The de Moivre distribution: another name for the normal distribution. The use of “de Moivre distribution” to describe the normal distribution is thought to originate with Freudenthal , who advocated the name because De Moivre was the first to define the distribution, in 1733 .
- The Elfving distribution is defined as
The distribution is named after Finnish statistician and mathematician Gustav Elfving (1908-1984), who described the distribution in 1947.
- The exceedance distribution function (EDF) is defined as 1 minus the cumulative distribution function (CDF) :
EDF = 1 – CDF
 Shakti, P. (2022). P-Distribution. Retrieved March 15, 2022 from: https://p-distribution.com/probability-distributions-list/
 G. Arfwedson, A probability distribution connected with Stirling’s second class numbers. Skand. Aktuarietidskr. 34 (1951), 121–132.
 Carlini, E. & Rapallo, F. (2013). Toric ideals with linear components: an algebraic interpretation of clustering the cells of a contingency table.
 Freudenthal, H. (1966b). Waarschijnlijkheid en Statistiek [Probability and Statistics]. Haarlem: De Erven F. Bohn.
 Daw, R. & Pearson, E. Studies in the History of Probability and Statistics. XXX. Abraham De Moivre’s 1733 Derivation of the Normal Curve: A Bibliographical Note. Biometrika Vol. 59, No. 3 (Dec., 1972), pp. 677-680 (4 pages)
Oxford University Press
Stephanie Glen. "Unusual Probability Distributions (You’ve Never Heard of)" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/unusual-probability-distributions-youve-never-heard-of/
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