Certain statistical distributions occur so often in applications that they are named. Examples include the binomial, exponential, normal, and uniform distributions. These distributions typically have parameters that allow for a certain degree of flexibility for modeling. Two important applications of these common statistical distributions are: (a) to provide a probability model the outcome of a random experiment, and (b) to provide a reasonable approximation to a data set.
Statistical distributions are traditionally introduced in separate sections in introductory probability texts, which obscures the fact that there are relationships between these distributions. The purpose of this section is to overview the various types of relationships between these common univariate distributions.
Common distributions and their relationships are presented in the encyclopedic work of Johnson et al. (1994, 1995) and Johnson et al. (2005). More concise treatments are given in Balakrishnan and...
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References and Further Reading
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Leemis, L.M. (2011). Relationships Among Univariate Statistical Distributions. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_487
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DOI: https://doi.org/10.1007/978-3-642-04898-2_487
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