Category: Uncategorized

  • 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 (1908-1984), 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 […]

  • Chi-Squared Distribution

    < Back to Probability Distribution List The chi-squared 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. […]

  • 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 T-Distribution (sometimes called the Student Distribution or T-Distribution) is a family of probability distributions that are similar in shape to the normal distribution. Student’s t-distribution 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 […]