Creating new distributions using integration and summation by parts

Abstract

Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the resulting pdfs are integrals that sometimes require computation as special functions. Summation by parts can be used similarly for discrete distributions. The general methodology is given, with some examples of distribution classes and of specific distributions, and fits to data.