Publisher : Korean Data and Information Science Society
DOI : 10.7465/jkdi.2015.26.6.1573
Title & Authors
Bayes estimation of entropy of exponential distribution based on multiply Type II censored competing risks data Lee, Kyeongjun; Cho, Youngseuk;
In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley`s approximate method is used to compute these estimators.We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.
Bayes estimate;competing risks;exponential distribution;multipy Type II censoring;
Baratpour, S., Ahmadi, J. and Arghami, N. R. (2007). Entropy properties of record statistics. Statistical Papers, 48, 197-213.
Cho, Y., Lee, C. and Shin, H. (2013). Estimation for the generalized exponential distribution under progressive type I interval censoring. Journal of the Korean Data & Information Science Society, 24, 1309-1317.
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.
Cho, Y., Sun, H. and Lee, K. (2015). Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy, 17, 101-122.
Cover, T. M. and Thomas, J. A. (2005). Elements of information theory, Wiley, Hoboken, NJ, USA.
Cox, D. (1959). The analysis of exponentially distributed lifetimes with two types of failure. Journal of the Royal Statistical Society B (Methodological), 21, 411-421.
DeGroot, M. H. (2005). Optimal statistical decision, John Wiley & Sons Inc., New York.
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.
Kwon, B., Lee, K. and Cho, Y. (2014). Estimation for the Rayleigh distribution based on Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 431-438.
Lawless, J. F. (2011). Statistical models and methods for lifetime data, Wiley, Hoboken.
Lee, K., Sun, H. and Cho, Y. (2014). Estimation of the exponential distribution based on multiply Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 633-641.
Lindley, D. (1980). Approximate Bayesian methods. Trabajos Estadistica, 31, 223-237.
Mao, S. and Sun, Y. (2014). Exact inference for competing risks model with generalized type I hybrid censored exponential data. Journal of Statistical Computation and Simulation, 84, 2506-2521.
Norstrom, J. (1996). The use of precautionary loss functions in risk analysis. Reliability, IEEE Transactions on, 45, 400-403.
Press, S. J. (2001). The subjectivity of scientists and the Bayesian approach, Wiley, New York.
Shin, H., Kim, J. and Lee, C. (2014). Estimation of the half-logistic distribution based on multiply Type I hybrid censored sample. Journal of the Korean Data & Information Science Society, 25, 1581-1589.
Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423.