Special Distribution

< List of probability distributions

The term “special distribution” refers to any probability distribution used frequently in practice. These distributions have special names and possess importance for their ability to model a range of real-life phenomena. They might also be associated with other special distributions through conditioning (an event treated as having occurred), limits (from calculus), or transformations. Consequently, these distributions are special because they are deemed “useful” or “important”. They commonly:

History of the special distribution

In 1892, Karl Pearson introduced the phrase “special distribution” in his book The Grammar of Science [1] to describe a probability distribution used to model specific phenomena. For instance, the normal distribution is a popular choice to model natural phenomena like height, weight, and IQ scores, owing to its symmetric and bell-shaped curve that centralizes most data around the mean. Pearson referred to certain probability distributions as more suitable to model phenomena than others, based on the idea of appropriateness. As a side note, Pearson also coined the term “standard deviation” [2].

Special distribution list

special distribution
The family of peaked normal distributions belong to the class of “special distributions” [3].


[1] K. Pearson. (1892). The Grammar of Science. (Third edition available here).

[2] Ramchandran, K. & Tsokos, C. Mathematical Statistics and Applications.

[3] Walli, G. (2010). Bayesian Variable Selection in Normal Regression Models. Thesis.

Scroll to Top