Methods for generating families of univariate continuous distributions in the recent decades

Carl Lee, Felix Famoye, Ayman Y. Alzaatreh

Research output: Contribution to journalReview articlepeer-review

85 Scopus citations


There has been a renewed interest in developing more flexible statistical distributions in recent decades. A major milestone in the methods for generating statistical distributions is undoubtedly the system of differential equation approach. There is a recent renewed interest in generating skewed distributions. Generally speaking, the methods developed prior to 1980s may be summarized into three categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be categorized as 'methods of combination' for the reason that these methods attempt to combine existing distributions into new distributions or adding new parameters to an existing distribution. This article discusses five general methods of combination and their variations. These five are (1) method of generating skew distributions, (2) method of adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed-transformer method, and (5) composite method.

Original languageEnglish
Pages (from-to)219-238
Number of pages20
JournalWiley Interdisciplinary Reviews: Computational Statistics
Issue number3
StatePublished - May 2013


  • Beta family
  • Composite distribution
  • Exponentiated family
  • Generalized distribution
  • Kw-generated family
  • Pearson system
  • Quantile method
  • Skew distribution
  • T-X family


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