
Poisson Distribution
< Back to Probability Distribution List A Poisson distribution, named for French mathematician Siméon Denis Poisson, predicts the occurrence of certain events in an interval (e.g., time, distance, volume) if you know how often the event has occurred. Most applications of the distribution are used to model the number of events happening in a fixed interval […]

Kullbach Distribution
< Back to Probability Distributions I love a good mystery. I found a reference to the Kullbach distribution while researching unusual probability distributions. Of course, the first thing I did was to perform a Google search for “Kullbach distribution”. I got exactly one result from Haight [1] So, what exactly is this mysterious distribution? A […]

Inverse Gamma Distribution
< Back to Probability Distribution List The inverse gamma distribution (or inverted gamma distribution) is commonly used for Bayesian analysis. It has the same distribution of the reciprocal of the gamma distribution. The shorthand X~inverted gamma(α, β), or IG(α, β), means that a random variable X has an inverse gamma distribution with positive parameters α and β. There […]

Exceedance Distribution
< Back to Probability Distribution List The exceedance distribution tells us how often we can expect rare events. The exceedance distribution function (EDF) is defined as 1 minus the cumulative distribution function (CDF) [1]: EDF = 1 – CDF The EDF, like the CDF, is bounded between 0 and 1. The CDF tells us what […]

Elfving distribution
< Back to Probability Distribution List The Elfving distribution is defined as [1] The distribution is named after Finnish statistician and mathematician Gustav Elfving (19081984), who described the distribution in 1947 [2]. In his Biometrika paper, Elfving established a distributional result concerning order statistics. Specifically, he investigates the distribution of the sample range when the […]

Exponential Distribution
< Back to Probability Distributions The exponential distribution, frequently used in reliability tests, describes time between events in a Poisson process, or time between elapsed events. It is a continuous analog of the geometric distribution [1]. The exponential distribution has a wide range of other applications, including in the Monte Carlo method, where random variables from a rectangular […]

Lexian Distribution
< Back to Probability Distributions List A Lexian distribution is another name for the binomial distribution (k, p) if p is not constant [1]. One way to interpret the distribution is as a special case of a mixture of binomial distributions [2]. The Lexian distribution considers a mixture distribution of subsets of binomials, each of which […]

ChiSquared Distribution
< Back to Probability Distribution List The chisquared distribution with k degrees of freedom is the distribution of a sum of the squares of k independent, standard normal random variables. It’s called a chi squared because it describes the summation of squares of the normally distributed random variables. The degrees of freedom (k) are equal to the number of samples being summed. […]

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. […]