Analysis of information measures using generalized type-Ⅰ hybrid censored data

Abstract

<abstract><p>An entropy measure of uncertainty has a complementary dual function called extropy. In the last six years, this measure of randomness has gotten a lot of attention. It cannot, however, be applied to systems that have survived for some time. As a result, the idea of residual extropy was created. To estimate the extropy and residual extropy, Bayesian and non-Bayesian estimators of unknown parameters of the exponentiated gamma distribution are generated. Bayesian estimators are regarded using balanced loss functions like the balanced squared error, balanced linear exponential and balanced general entropy. We use the Lindley method to get the extropy and residual extropy estimates for the exponentiated gamma distribution based on generalized type-Ⅰ hybrid censored data. To test the effectiveness of the proposed methodologies, a simulation experiment was carried out, and the actual data set was studied for illustrative purposes. In summary, the mean squared error values decrease as the number of failures increases, according to the results obtained. The Bayesian estimates of residual extropy under the balanced linear exponential loss function perform well compared to the other estimates. Alternatively, the Bayesian estimates of the extropy perform well under a balanced general entropy loss function in the majority of situations.</p></abstract>

Dynamic Weighted Cumulative Residual Entropy Estimators for Laplace Distribution: Bayesian Approach

“…The Bayesian and non-Bayesian estimation of dynamic cumulative residual Tsallis entropy for moment exponential distribution under progressive censored type II is discussed by Alyami et al (3) . Helmy et al (4) described the analysis of information measures using generalized type -I hybrid censored data. Entropy estimation is mainly inconvenient, when there are less samples relative to the total number of symbols.…”

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

“…This plan has previously been covered in several literary works, see, for example, those by Balakrishnan and Kundu, 3 Huang and Yang, 4 Habibi Rad and Izanlo, 5 Panahi and Sayyareh, 6 Jeon and Kang, 7 Sarkar and Tripathy, 8 and Dutta et al 9 Recently, many researchers have been interested in using different types of schemes using many lifetime models through many applications. For more details, see the works by Nassar et al, 10 Nassr and Elharoun, 11 Hassan et al, 12 Nassr and Azm, 13 El Azm et al, 14 Yousef et al, 15 Elgarhy et al, 16,17 Bantan et al, 18,19 Elbatal et al, 20 Shrahili et al, 21 Algarni et al, 22 Alotaibi et al, 23 Ahmadini et al, 24 Mohamed et al, 25 Abdelwahab et al, 26 Alyami et al, 27 Helmy et al, 28 Hassan and Nassr, 29,30 and Abd-Elfattah et al 31 The Gompertz distribution, first proposed by Benjamin Gompertz as a model for the distribution of income in Ref. 32, is considered to represent the underlying distribution in this study.…”