Estimation in the Complementary Exponential Geometric Distribution Based on Progressive Type-II Censored Data
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Estimation in the Complementary Exponential Geometric Distribution Based on Progressive Type‑II Censored Data Özlem Gürünlü Alma1 · Reza Arabi Belaghi2 Received: 15 July 2017 / Revised: 12 November 2018 / Accepted: 19 March 2019 © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract Complementary exponential geometric distribution has many applications in survival and reliability analysis. Due to its importance, in this study, we are aiming to estimate the parameters of this model based on progressive type-II censored observations. To do this, we applied the stochastic expectation maximization method and Newton–Raphson techniques for obtaining the maximum likelihood estimates. We also considered the estimation based on Bayesian method using several approximate: MCMC samples, Lindely approximation and Metropolis–Hasting algorithm. In addition, we considered the shrinkage estimators based on Bayesian and maximum likelihood estimators. Then, the HPD intervals for the parameters are constructed based on the posterior samples from the Metropolis– Hasting algorithm. In the sequel, we obtained the performance of different estimators in terms of biases, estimated risks and Pitman closeness via Monte Carlo simulation study. This paper will be ended up with a real data set example for illustration of our purpose. Keywords Bayesian analysis · Complementary exponential geometric (CEG) distribution · Progressive type-II censoring · Maximum likelihood estimators · SEM algorithm · Shrinkage estimator Mathematics Subject Classification 62N01 · 62N02
1 Introduction Complementary risk (CR) problems arise naturally in a number of context, especially in problem of survival analysis, actuarial science, demography and industrial reliability [6]. In the classical complementary risk scenarios, the event of interest is related to * Özlem Gürünlü Alma [email protected] Reza Arabi Belaghi [email protected] 1
Department of Statistics, Faculty of Sciences, Muğla Sıtkı Koçman University, Muğla, Turkey
2
Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
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Ö. Gürünlü Alma, R. Arabi Belaghi
causes which are not completely observed. Therefore, the lifetime of the event of interest is modeled as function of the available information, which is only the maximum ordered lifetime value among all causes. In the presence of CR in survival analysis, the risks are latent in the sense that there is no information about which factor was responsible for component failure, we observe only the maximum lifetime value among all risks. For example, when studying death on dialysis, receiving a kidney transplant is an event that competes with the event of interest such as heart failure, pulmonary embolism and stroke. In reliability, it observed only the maximum component lifetime of a parallel system, that is, the observable quantities for each component are the maximum lifetime va
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