Browse > Article
http://dx.doi.org/10.29220/CSAM.2020.27.4.469

Bayesian and maximum likelihood estimation of entropy of the inverse Weibull distribution under generalized type I progressive hybrid censoring  

Lee, Kyeongjun (Division of Mathematics and Big Data Science, Daegu University)
Publication Information
Communications for Statistical Applications and Methods / v.27, no.4, 2020 , pp. 469-486 More about this Journal
Abstract
Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.
Keywords
generalized type I progressive hybrid censoring; inverse Weibull distribution; Lindley approximation; maximum likelihood estimation; maximum product spacings estimation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Baratpour S, Ahmadi J, and Arghami NR (2007). Entropy properties of record statistics, Statistical Papers, 48, 197-213.   DOI
2 Basu AP and Ebrahimi N (1991). Bayesian approach to life testing and reliability estimation using asymmetric loss function, Journal of Statistical Planning and Inference, 29, 21-31.   DOI
3 Calabria R and Pulcini G (1990). On the maximum likelihood and lease squares estimation in inverse Weibull distribution, Statistics Applicata, 2, 53-66.
4 Calabria R and Pulcini G (1994). Bayes 2-sample prediction for the inverse Weibull distribution, Communications in Statistics - Theory and Methods, 23, 1811-1824.   DOI
5 Cheng RCH and Amin NAK (1983). Estimating parameters in continuous univariate distributions with a shifted origin, Journal of the Royal Statistical Society B, 45, 394-403.
6 Cho Y, Sun H, and Lee K (2014). An estimation of the entropy for a Rayleigh distribution based on doubly-generalized type-II hybrid censored samples, Entropy, 16, 3655-3669.   DOI
7 Cho Y, Sun H, and Lee K (2015a). Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring, Entropy, 17, 101-122.
8 Cho Y, Sun H, and Lee K (2015b). Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme, Statistical Methodology, 23, 18-34.   DOI
9 Cover TM and Thomas JA (2005). Elements of Information Theory, Wiley, Hoboken, NJ.
10 Huzurbazar VS (1948). The likelihood equation, consistency and the maxima of the likelihood function, Annals of Eugenics, 14, 185-200.   DOI
11 Kang S, Cho Y, Han J, and Kim J (2012). An estimation of the entropy for a double exponential distribution based on multiply type-II censored samples, Entropy, 14, 161-173.   DOI
12 Keller AZ, Giblin MT, and Farnworth NR (1985). Reliability analysis of commercial vehicle engines, Reliability Engineering, 10, 89-102.
13 Blischke WR and Murthy DNP (2000). Reliability : Modeling, Prediction, and Optimization, Wiley, New York.
14 Khan MS, Pasha GR, and Pasha AH (2008). Theoretical analysis of inverse Weibull distribution, WSEAS Transactions on Mathematics, 7, 30-38.
15 Lee K (2017). Estimation of entropy of the inverse Weibull distribution under generalized progressive hybrid censored data, Journal of the Korean Data & Information Science Society, 28, 659-668.   DOI
16 Varian HR (1975). A Bayesian Approach to Real Estate Assessment, North-Holland Publishing Company, Amsterdam.
17 Nassar MM and Eissa FH (2004). Bayesian estimation for the exponentiated Weibull model, Communications in Statistics - Theory and Methods, 33, 2343-2362.   DOI
18 Norstrom J (1996). The use of precautionary loss functions in risk analysis, IEEE Transactions on Reliability, 45, 400-403.   DOI
19 Shannon CE (1948). A mathematical theory of communication, The Bell System Technical Journal, 27, 379-423.   DOI