Model Assisted Statistics and Applications 13 (2018) 107–121 107 DOI 10.3233/MAS-180423 IOS Press Survival estimation in xgamma distribution under progressively type-II right censored scheme Subhradev Sen a,∗ , N. Chandra b and Sudhansu S. Maiti c a Alliance School of Business, Alliance University, Bengaluru, India b Department of Statistics, Pondicherry University, Puducherry, India c Department of Statistics, Visva-Bharati University, Santiniketan, India Abstract. In this article, we have investigated some further distributional properties (such as, characteristic and generating func- tions, distributions of extreme order statistics, important entropy measures) and some additional survival and/or reliability charac- teristics (such as, time to failure, ageing intensity, stress-strength reliability) of one parameter xgamma distribution which serves as an useful survival model. We also studied the estimation procedures of the model parameter and its important survival charac- teristics considering maximum likelihood and Bayesian techniques under progressively type-II right censoring scheme. Interval estimation and coverage probability for the parameter were obtained based on maximum likelihood estimation. A Monte-Carlo simulation study was conducted to compare performance of the various estimates. Progressively type-II censoring scheme was considered in view of cost and time constraints. A real data were also analyzed for illustrating the methods described in the paper. Keywords: Lifetime distribution, survival analysis, progressive censoring, maximum likelihood, Bayes method AMS Classification: MSC 62E10, MSC 62N02, MSC 62F15 1. Introduction In a wide variety of scientific and technological fields, such as public health, actuarial science, biomedical studies, demography, and industrial reliability, modeling and analysis of lifetimes is an important aspect of statistical work. The failure behavior of any system can be considered as a random variable due to the variations from one system to another resulting from the types and nature of the various systems or processes. Therefore, it seems logical to find a statistical model for the failure of the system. In other applications, survival data are categorized by their failure rate, e.g., the number of observable events per unit in a period of time. Survival data are categorized by their failure rate which can be monotone (non-increasing and non-decreasing) or non-monotone (bathtub and upside-down bathtub, or unimodal). For modeling of such survival data, many models have been proposed in the literature based on failure rate types. Exponential, gamma, Weibull and lognormal are well established probability distributions for modeling real world phenomena, especially in modeling lifetime (or time-to-event) of any system or unit. In recent years, Lindley distribution (see Lindley, 1958) has drawn attention of the researchers and practitioners in modeling time-to-event data sets (see Ghitany et al., 2008; Mazucheli & Achcar, 2011; Gómez & Calderin, 2011; and references therein for more details). * Corresponding author: Subhradev Sen, Alliance School of Business, Alliance University, City Campus 2, 2nd Cross, 36th Main, Dollars Scheme, BTM 1st Stage, Bangalore 560068, India. Tel.: +91 9946186231; E-mail: subhradev.stat@gmail.com. ISSN 1574-1699/18/$35.00 c  2018 – IOS Press and the authors. All rights reserved