Estimation of Tsallis entropy for exponentially distributed several populations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913198771273728 |
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| author | Kumar, Naveen Dixit, Ambesh Vijay, Vivek |
| author_facet | Kumar, Naveen Dixit, Ambesh Vijay, Vivek |
| contents | We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved estimate, establishing the inadmissibility of the best affine equivariant estimate of the parameter function. A class of smooth estimates utilizing the Brewster technique is obtained, resulting in a significant improvement in the risk value. We computed the Brewster-Zidek estimates for both one and two populations, to illustrate the comparison with best affine equivariant and Stein-type estimates. We further derive that the Bayesian estimate, employing an inverse gamma prior, which takes the best affine equivariant estimate as a particular case. We provide a numerical illustration utilizing simulated samples for a single population. The purpose is to demonstrate the impact of sample size, location parameter, and entropic index on the estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimation of Tsallis entropy for exponentially distributed several populations Kumar, Naveen Dixit, Ambesh Vijay, Vivek Statistics Theory We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved estimate, establishing the inadmissibility of the best affine equivariant estimate of the parameter function. A class of smooth estimates utilizing the Brewster technique is obtained, resulting in a significant improvement in the risk value. We computed the Brewster-Zidek estimates for both one and two populations, to illustrate the comparison with best affine equivariant and Stein-type estimates. We further derive that the Bayesian estimate, employing an inverse gamma prior, which takes the best affine equivariant estimate as a particular case. We provide a numerical illustration utilizing simulated samples for a single population. The purpose is to demonstrate the impact of sample size, location parameter, and entropic index on the estimates. |
| title | Estimation of Tsallis entropy for exponentially distributed several populations |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2401.09009 |