Mathematics and Statistics Vol. 9(5), pp. 780 - 791
DOI: 10.13189/ms.2021.090518
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Estimating the Entropy and Residual Entropy of a Lomax Distribution under Generalized Type-II Hybrid Censoring

Mahmoud Riad Mahmoud ¹, Moshera. A. M. Ahmad ², Badiaa. S. Kh. Mohamed ^3,*
1 Department of Mathematical Statistics, Institute of Statistics Studies and Research, Cairo University, Giza, Egypt
² El Gazeera High Institute For Computer & Management Information System, Egypt
³ Department of Mathematical Statistics, Institute of Statistical Studies & Research, Cairo University, Giza, Egypt

ABSTRACT

The Lomax distribution (or Pareto II) was first introduced by K. S. Lomax in 1954. It can be readily applied to a wide range of situations including applications in the analysis of the business failure life time data, economics, and actuarial science, income and wealth inequality, size of cities, engineering, lifetime, and reliability modeling. In his pioneering paper, Shannon 1948 defined the notion of entropy as a mathematical measure of information, which is sometimes called Shannon entropy in his honor. He laid the groundwork for a new branch of mathematics in which the notion of entropy plays a fundamental role over different areas of applications such as statistics, information theory, financial analysis, and data compression. [Ebrahimi and Pellerey 14] introduced the residual entropy function because the entropy shouldn't be applied to a system that has survived for some units of time, and therefore, the residual entropy is used to measure the ageing and characterize, classify and order lifetime distributions. In this paper, the estimation of the entropy and residual entropy of a two parameter Lomax distribution under a generalized Type-II hybrid censoring scheme are introduced. The maximum likelihood estimation for the entropy is provided and the Bayes estimation for the residual entropy is obtained. Simulation studies to assess the performance of the estimates with different sample sizes are described, finally conclusions are discussed.

KEYWORDS
The Entropy, Residual Entropy, Lomax Distribution, Generalized Type-II Hybrid Censoring, The Maximum Likelihood and Bayes Estimation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mahmoud Riad Mahmoud , Moshera. A. M. Ahmad , Badiaa. S. Kh. Mohamed , "Estimating the Entropy and Residual Entropy of a Lomax Distribution under Generalized Type-II Hybrid Censoring," Mathematics and Statistics, Vol. 9, No. 5, pp. 780 - 791, 2021. DOI: 10.13189/ms.2021.090518.

(b). APA Format:
Mahmoud Riad Mahmoud , Moshera. A. M. Ahmad , Badiaa. S. Kh. Mohamed (2021). Estimating the Entropy and Residual Entropy of a Lomax Distribution under Generalized Type-II Hybrid Censoring. Mathematics and Statistics, 9(5), 780 - 791. DOI: 10.13189/ms.2021.090518.