Moment-based approximations of distributions using mixtures: Theory and applications

Bruce G. Lindsay, Ramani S. Pilla, Prasanta Basak

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


There are a number of cases where the moments of a distribution are easily obtained, but theoretical distributions are not available in closed form. This paper shows how to use moment methods to approximate a theoretical univariate distribution with mixtures of known distributions. The methods are illustrated with gamma mixtures. It is shown that for a certain class of mixture distributions, which include the normal and gamma mixture families, one can solve for a p-point mixing distribution such that, the corresponding mixture has exactly the same first 2p moments as the targeted univariate distribution. The gamma mixture approximation to the distribution of a positive weighted sums of independent central χ2 variables is demonstrated and compared with a number of existing approximations. The numerical results show that the new approximation is generally superior to these alternatives.

Original languageEnglish (US)
Pages (from-to)215-230
Number of pages16
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability


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