Recent Development of Methods for Generating Univariate Continuous Distributions

Abstract

Development of new statistical distributions is an old topic. A major milestone is undoubtedly the system of differential equation approach. The literatures indicate the approaches of generating new families of distributions are quite different before and after 1980. Generally speaking, the methods developed prior to 1980 may be summarized into three major categories: (1) method of differential equation, (2) method of transformation, and (3) quantile method. Techniques developed since 1980s may be summarized 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 talk will give a quick survey of the three methods proposed prior to 1980, and discuss five methods developed after 1980.