期刊
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
卷 52, 期 2, 页码 215-230出版社
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1004105603806
关键词
cumulants; cumulative distribution function; gamma mixtures; mixture distribution; moment matrix; p-point mixture; tail probability; weighted sums of chi-squares
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 chi(2) 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.
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