On a Characterization of Exponential and Double Exponential Distributions
Recently, G. Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev’s theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, o...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2025-02-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/530 |
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| _version_ | 1832086567160643584 |
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| author | Reza Rastegar Alexander Roitershtein |
| author_facet | Reza Rastegar Alexander Roitershtein |
| author_sort | Reza Rastegar |
| collection | DOAJ |
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Recently, G. Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev’s theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, obtain a similar characterization for the Laplace family of distributions.
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| format | Article |
| id | doaj-art-411442d241a04de99af3dc83cc1cc9df |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-411442d241a04de99af3dc83cc1cc9df2025-02-06T10:52:38ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-02-0123110.57805/revstat.v23i1.530On a Characterization of Exponential and Double Exponential DistributionsReza Rastegar0Alexander Roitershtein1Occidental Petroleum CorporationTexas A&M University Recently, G. Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev’s theorem by relaxing a restriction on the sign of mixture coefficients and, in addition, obtain a similar characterization for the Laplace family of distributions. https://revstat.ine.pt/index.php/REVSTAT/article/view/530hypoexponential distributionLaplace distributioncharacterization of distributionssums of independent random variablescharacteristic functionsfunctional equations |
| spellingShingle | Reza Rastegar Alexander Roitershtein On a Characterization of Exponential and Double Exponential Distributions Revstat Statistical Journal hypoexponential distribution Laplace distribution characterization of distributions sums of independent random variables characteristic functions functional equations |
| title | On a Characterization of Exponential and Double Exponential Distributions |
| title_full | On a Characterization of Exponential and Double Exponential Distributions |
| title_fullStr | On a Characterization of Exponential and Double Exponential Distributions |
| title_full_unstemmed | On a Characterization of Exponential and Double Exponential Distributions |
| title_short | On a Characterization of Exponential and Double Exponential Distributions |
| title_sort | on a characterization of exponential and double exponential distributions |
| topic | hypoexponential distribution Laplace distribution characterization of distributions sums of independent random variables characteristic functions functional equations |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/530 |
| work_keys_str_mv | AT rezarastegar onacharacterizationofexponentialanddoubleexponentialdistributions AT alexanderroitershtein onacharacterizationofexponentialanddoubleexponentialdistributions |