Distribution Fitting Introductory Overview - General Purpose

Distribution Fitting

In some research applications, you can formulate hypotheses about the specific distribution of the variable of interest. For example, variables whose values are determined by an infinite number of independent random events will be distributed following the normal distribution: you can think of a person's height as being the result of very many independent factors such as numerous specific genetic predispositions, early childhood diseases, nutrition, etc. (see the animation below for an example of the normal distribution). As a result, height tends to be normally distributed in the U.S. population. On the other hand, if the values of a variable are the result of very rare events, then the variable will be distributed according to the Poisson distribution (sometimes called the distribution of rare events). For example, industrial accidents can be thought of as the result of the intersection of a series of unfortunate (and unlikely) events, and their frequency tends to be distributed according to the Poisson distribution. These and other distributions are described in greater detail in the respective glossary topics.

Animated Normal Distribution

Another common application where distribution fitting procedures are useful is when you want to verify the assumption of normality before using some parametric test (see General Purpose of Nonparametric Tests). For example, you may want to use the Kolmogorov-Smirnov test for normality or the Shapiro-Wilks W test to test for normality.