Estimation of Shannon entropy of the inverse exponential Rayleigh model under progressively Type-Ⅱ censored test

Haiping Ren; Ziwen Zhang; Qin Gong; Haiping Ren; Ziwen Zhang; Qin Gong

doi:10.3934/math.2025434

AIMS Mathematics

2025, Volume 10, Issue 4: 9378-9414. doi: 10.3934/math.2025434

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Estimation of Shannon entropy of the inverse exponential Rayleigh model under progressively Type-Ⅱ censored test

1.
Teaching Department of Basic Subjects, Jiangxi University of Science and Technology, Nanchang, 330013, China
2.
College of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China

Received: 08 February 2025 Revised: 01 April 2025 Accepted: 03 April 2025 Published: 23 April 2025
MSC : 62E10, 62F10

In this paper, we investigate the problem of entropy estimation for the inverse exponential Rayleigh distribution under progressively Type-Ⅱ censored samples. For the Shannon entropy of the inverse Rayleigh distribution, the maximum likelihood estimation and Bayesian estimation are studied, as well as the interval estimation. Under the Bayesian method, we used three different loss functions to discuss the Shannon entropy under each of these loss functions. The three loss functions are as follows: the weighted squared error loss function, the K-loss function, and the precautionary loss function. The Bayesian estimates of Shannon's entropy under these three loss functions are computed using the Lindley approximation and mixed Gibbs sampling. Finally, we calculated the estimated values, mean squared errors, and variances of the estimators through Monte Carlo simulations. To evaluate the performance of the estimation methods, we chose to use the mean squared errors for a comparative analysis. In the subsequent step, we applied the estimated results to a real dataset.
- Bayesian estimation,
- inverse exponential Rayleigh distribution,
- loss function,
- Shannon entropy
Citation: Haiping Ren, Ziwen Zhang, Qin Gong. Estimation of Shannon entropy of the inverse exponential Rayleigh model under progressively Type-Ⅱ censored test[J]. AIMS Mathematics, 2025, 10(4): 9378-9414. doi: 10.3934/math.2025434

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Abstract

In this paper, we investigate the problem of entropy estimation for the inverse exponential Rayleigh distribution under progressively Type-Ⅱ censored samples. For the Shannon entropy of the inverse Rayleigh distribution, the maximum likelihood estimation and Bayesian estimation are studied, as well as the interval estimation. Under the Bayesian method, we used three different loss functions to discuss the Shannon entropy under each of these loss functions. The three loss functions are as follows: the weighted squared error loss function, the K-loss function, and the precautionary loss function. The Bayesian estimates of Shannon's entropy under these three loss functions are computed using the Lindley approximation and mixed Gibbs sampling. Finally, we calculated the estimated values, mean squared errors, and variances of the estimators through Monte Carlo simulations. To evaluate the performance of the estimation methods, we chose to use the mean squared errors for a comparative analysis. In the subsequent step, we applied the estimated results to a real dataset.

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