期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：04
出版社：Indian Statistical Institute
摘要：In this paper we consider mixtures of distributions from a natural exponential family. Using an adequate basis of polynomials we obtain an expression for the difference between the mixed density and its parent. This technique is applied to evaluate the distance of the mixture from the parent distribution in $L^2$-norm. Bounds are also derived in $L^1$-norm and for the difference between distribution functions. We illustrate the results by some examples through gamma, Poisson and normal mixtures. Finally, more general refined approximations of the mixture density are proposed and illustrated through a Poisson mixture model.
关键词：$L^1$ and $L^2$-norm, mixed gamma distribution, mixed Poisson distribution, mixed normal distribution, orthogonal polynomials.
