Estimation in the Complementary Exponential Geometric Distribution Based on Progressive Type-II Censored Data

• Published in: Communications in mathematics and statistics Vol. 8; no. 4; pp. 409 - 441
• Main Authors: Gürünlü Alma, Özlem, Arabi Belaghi, Reza
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020; Springer Nature B.V
• Subjects: Algorithms; Approximation; Bayesian analysis; Censored data (mathematics); Mathematics; Mathematics and Statistics; Maximum likelihood estimates; Maximum likelihood estimators; Monte Carlo simulation; Parameter estimation; Reliability analysis; Statistics; 62N01; 62N02; Progressive type-II censoring; Shrinkage estimator; Maximum likelihood estimators; Bayesian analysis; Complementary exponential geometric (CEG) distribution; SEM algorithm
• ISSN: 2194-6701; 2194-671X
• DOI: 10.1007/s40304-019-00181-8

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.