
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. […]

Normal Distribution
< Back to Probability Distribution List A normal distribution, denoted Ν (μ, σ2) is a symmetrical, bellshaped distribution. It’s widely used in business and statistics because many reallife phenomena fit a bellcurve shape like heights of people, blood pressure readings, or standardized test scores like the SAT. The empirical rule, depicted above, tells you what percentage of normally […]

Triangular Distribution (Symmetric)
< Back to List of Distributions A triangular distribution (or triangle distribution) is a continuous probability distribution defined by three parameters: a: the minimum or lower limit, (a ≤ c), c: the mode (height or peak), (a ≤ c ≤ b), b: the maximum or upper limit (b ≥ c). When a and b are equal but opposite in sign […]

Cauchy Distribution
< Back to Probability Distribution List The Cauchy distribution (also called the Lorentz distribution, Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution) is a family of continuous probably distributions named after Augustin Cauchy. They resemble the normal distribution with a taller peak. Unlike the normal distribution, its fat tails decay much more slowly. The distribution, which describes resonance behavior, is well known for the fact […]

Kapetyn Distribution
< Back to Probability Distributions List The 1962 National Bureau of Standards Report lists the Kapetyn distribution as another name for a generalized normal distribution. There are sparse references to the Kapetyn distribution as a synonym for the “generalized” normal outside of the NBS report. The generalized family of normal distributions is a very large […]

Stuttering Poisson Distribution
< Back to Probability Distributions List The Stuttering Poisson Distribution (SPD) is a nonnegative discrete compound Poisson distribution that describes two or more events that happen in quickly in bursts. For example, the events might occur in groups or batches [1]. The distribution has the probability generating function (PGF): Where Px is the probability a […]

PollaczekGeiringer Distribution
< Back to Probability Distribution List The PollaczekGeiringer distribution is another name for the stuttering Poisson Distribution (SPD), a nonnegative discrete compound probability distribution [1]. Historical Notes on the PollaczekGeiringer Distribution The PollaczekGeiringer distribution makes a sparse entry in [2] The reference [17] No. 9 refers to the obscure and seldomreference book A Summary of […]