A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle
We consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called “mean orthogonal class” is closed under convolution. A previous characteriza...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/468418 |
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| _version_ | 1850174774544695296 |
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| author | Werner Hürlimann |
| author_facet | Werner Hürlimann |
| author_sort | Werner Hürlimann |
| collection | DOAJ |
| description | We consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called “mean orthogonal class” is closed under convolution. A previous characterization of the compound gamma characterization of random sums is revisited and clarified. A new characterization of the compound distribution with multiparameter Hermite count distribution and gamma severity distribution is obtained. |
| format | Article |
| id | doaj-art-d7295f3edfdc4f2bbfb08667121c1010 |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-d7295f3edfdc4f2bbfb08667121c10102025-08-20T02:19:34ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/468418468418A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s PrincipleWerner Hürlimann0Wolters Kluwer Financial Services, Seefeldstrasse 69, 8008 Zürich, SwitzerlandWe consider the class of those distributions that satisfy Gauss's principle (the maximum likelihood estimator of the mean is the sample mean) and have a parameter orthogonal to the mean. It is shown that this so-called “mean orthogonal class” is closed under convolution. A previous characterization of the compound gamma characterization of random sums is revisited and clarified. A new characterization of the compound distribution with multiparameter Hermite count distribution and gamma severity distribution is obtained.http://dx.doi.org/10.1155/2013/468418 |
| spellingShingle | Werner Hürlimann A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle The Scientific World Journal |
| title | A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle |
| title_full | A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle |
| title_fullStr | A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle |
| title_full_unstemmed | A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle |
| title_short | A Characterization of the Compound Multiparameter Hermite Gamma Distribution via Gauss’s Principle |
| title_sort | characterization of the compound multiparameter hermite gamma distribution via gauss s principle |
| url | http://dx.doi.org/10.1155/2013/468418 |
| work_keys_str_mv | AT wernerhurlimann acharacterizationofthecompoundmultiparameterhermitegammadistributionviagausssprinciple AT wernerhurlimann characterizationofthecompoundmultiparameterhermitegammadistributionviagausssprinciple |