
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 […]

Romanovsky Distribution
< Back to Probability Distribution List The name “Romanovsky distribution” has been used as another name for the negative hypergeometric distribution [1]. It is also used to describe a restricted occupancy distribution in “ball and urn” investigations [2]. Historical Notes on the Romanovsky Distribution Haight [3] lists Romanovsky’s distribution in the index yet points to […]

Tine Distribution
< Back to Probability Distribution List The Tine distribution (sometimes called symmetric triangular distribution) made an entry in the Index to the Distributions of Mathematical Statistics [1] as: The Annals of Mathematical Statistics [2] contains an expanded definition: Rinne [3] defines Tine’s distribution as the distribution of two independent and identically distributed uniform variables (i.e., […]

GramCharlier Distribution
< Back to Probability Distribution List The GramCharlier distribution is a way to explicitly model departure from normality by using a series expansion around a normal distribution. It is more flexible than a normal distribution because it directly introduces a distribution’s kurtosis and skew as unknown parameters. The One practical application of the GramCharlier distribution […]

RadicoNormal Distribution
< Back to Probability Distributions List The Radiconormal distribution is a member of the modified normal distributions constructed by Romanowski [1]. It is a special case of the modified normal cumulative density function (CDF) [1] with a = ½. Note that when a is infinitely large, the curve is a normal distribution. When a tends […]