caa a22 4500 475827015 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004105603806 doi (NATIONALLICENCE)springer-10.1023/A:1004105603806 Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications [Elektronische Daten] [Bruce Lindsay, Ramani Pilla, Prasanta Basak] 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. The Institute of Statistical Mathematics, 2000 Cumulants nationallicence cumulative distribution function nationallicence gamma mixtures nationallicence mixture distribution nationallicence moment matrix nationallicence p -point mixture nationallicence tail probability nationallicence weighted sums of chi-squares nationallicence Lindsay Bruce Department of Statistics, 326 Classroom Building, Pennsylvania State University, University Park, 16802, PA-, U.S.A. aut Pilla Ramani National Institutes of Health, 6100 Executive Blvd., Room 7B-13, MSC 7510, 20892-7510, Bethesda, MD, U.S.A. aut Basak Prasanta 120 Eiche Library, The Pennsylvania State University, Altoona Campus, 16601, Altoona, PA-, U.S.A aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 215-230 0020-3157 52:2<215 2000 52 10463 https://doi.org/10.1023/A:1004105603806 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004105603806 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lindsay Bruce Department of Statistics, 326 Classroom Building, Pennsylvania State University, University Park, 16802, PA-, U.S.A aut NATIONALLICENCE 700 1- Pilla Ramani National Institutes of Health, 6100 Executive Blvd., Room 7B-13, MSC 7510, 20892-7510, Bethesda, MD, U.S.A aut NATIONALLICENCE 700 1- Basak Prasanta 120 Eiche Library, The Pennsylvania State University, Altoona Campus, 16601, Altoona, PA-, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 215-230 0020-3157 52:2<215 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer