Using Gamma Distribution to Obtain Maxwell–Rényi Statistics and Other Generalized Distributions
A universal method is proposed for performing calculations within the framework of generalized statistics generated by the parametric Tsallis, Rényi, and Sharma–Mittal entropies. The essence of the approach lies in the use of an auxiliary gamma distribution whose parameters correspond to a particula...
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| Veröffentlicht in: | Moscow University physics bulletin 2024-08, Vol.79 (4), p.439-449 |
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| container_title | Moscow University physics bulletin |
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| creator | Nakashidze, D. V. Savchenko, A. M. Bakiev, T. N. |
| description | A universal method is proposed for performing calculations within the framework of generalized statistics generated by the parametric Tsallis, Rényi, and Sharma–Mittal entropies. The essence of the approach lies in the use of an auxiliary gamma distribution whose parameters correspond to a particular variant of the statistics. Equations are derived that allow the generalised partition function and the mean energy to be expressed in terms of canonical quantities. The effectiveness of the proposed method is demonstrated using the example of Rényi statistics. The Maxwell–Rényi distribution is obtained and its properties are calculated, based on which assumptions about the possible nature of the generalised parameter are formulated. |
| doi_str_mv | 10.3103/S0027134924700589 |
| format | Article |
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The Maxwell–Rényi distribution is obtained and its properties are calculated, based on which assumptions about the possible nature of the generalised parameter are formulated.</description><identifier>ISSN: 0027-1349</identifier><identifier>EISSN: 1934-8460</identifier><identifier>DOI: 10.3103/S0027134924700589</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Energy distribution ; Mathematical and Computational Physics ; Parameters ; Partitions (mathematics) ; Physics ; Physics and Astronomy ; Probability distribution functions ; Statistics ; Theoretical ; Theoretical and Mathematical Physics</subject><ispartof>Moscow University physics bulletin, 2024-08, Vol.79 (4), p.439-449</ispartof><rights>Allerton Press, Inc. 2024. ISSN 0027-1349, Moscow University Physics Bulletin, 2024, Vol. 79, No. 4, pp. 439–449. © Allerton Press, Inc., 2024. 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The Maxwell–Rényi distribution is obtained and its properties are calculated, based on which assumptions about the possible nature of the generalised parameter are formulated.</description><subject>Energy distribution</subject><subject>Mathematical and Computational Physics</subject><subject>Parameters</subject><subject>Partitions (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Probability distribution functions</subject><subject>Statistics</subject><subject>Theoretical</subject><subject>Theoretical and Mathematical Physics</subject><issn>0027-1349</issn><issn>1934-8460</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kE1KAzEYhoMoWKsHcBdwPZq_mUmWUrUKlYK16yF_U1OmmZqkaF15B0_hObyJJ3FKBRFx9S3e53k_eAE4xuiUYkTPJgiRElMmCCsRyrnYAT0sKMs4K9Au6G3ibJPvg4MY5x1SECp6QE2j8zM4lIuFhBcupuDUKrnWw9TCsUrSeXgrn59s03y-vt19vPu1g5MkU4c6HaH0Bo7Tgw1waL0NsnEv1vwqiodgr5ZNtEfftw-mV5f3g-tsNB7eDM5HmcaCp4yUQtDaElVwTlDOLLUMC10wro0VBVJGm1qwQlOuWEmNlFwpU9O61hjbnNA-ONn2LkP7uLIxVfN2FXz3sqIY54jQvMw7Cm8pHdoYg62rZXALGdYVRtVmyurPlJ1Dtk7sWD-z4af5f-kL1s54UA</recordid><startdate>20240801</startdate><enddate>20240801</enddate><creator>Nakashidze, D. 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| ispartof | Moscow University physics bulletin, 2024-08, Vol.79 (4), p.439-449 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Energy distribution Mathematical and Computational Physics Parameters Partitions (mathematics) Physics Physics and Astronomy Probability distribution functions Statistics Theoretical Theoretical and Mathematical Physics |
| title | Using Gamma Distribution to Obtain Maxwell–Rényi Statistics and Other Generalized Distributions |
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