Appl. Math. Inf. Sci. 14, No. 5, 1-16 (2020) 1 Applied Mathematics & Information Sciences An International Journal http://dx.doi.org/10.18576/amis/”papernew” Parameter Estimation for the Generalized Linear Exponential Distribution Based on Progressively Type-Π Hybrid Censored Data M. A. W. Mahmoud 1 , N. M. Yhiea 2,∗ and SH. M. EL-SAID 3 1 Department of Mathematics, Faculty of Science Al-Azhar University Naser City (11884), Cairo, Egypt. 2 Department of Mathematics, Faculty of Science, Suez Canal University. Ismailia, Egypt Received: 21 May 2020, Revised: 27 Jul. 2020, Accepted: 22 Aug. 2020 Published online: 1 Sep. 2020 Abstract: Estimations of the unknown parameters of the generalized linear exponential distribution (GLED) using type-Π progressive hybrid censored (HC) data are obtained. The maximum likelihood estimation (MLE) and Bayes estimation for all parameters and some lifetime funvtions (reliability, hazard function and reversed hazard function) are obtained. Also, we apply Markov chain Monte Carlo (MCMC) technique and Lindely’s approximation technique to carry out a Bayesian estimation. Under the assumptions of informative and non-informative priors, estimates of Bayes and credible intervals are obtained. Different methods have been compared using Mont Carlo simulations. Real data set has been studied for illustrative purpose. Keywords: Hybrid censoring scheme(HCS), Generalized Linear Exponential Distribution (GLE) Bayes Estimators, Maximum Likelihood Estimation (MLE),Lindely approximation, Markov Chain Monte Carlo (MCMC) 1 Introduction In parametric estimation problems, we often assume that a set of randomly selected samples of pre-speciﬁed number of units, say n, is available. It is further assumed that random observations follow a speciﬁed distribution. But in practice, observations on all the units may not be available because observations corresponding to some units are either not recorded or lost during intermediate transmission. The resulting data are termed as censored sample. The two most common and popular censoring schemes are Type-I and type-II censoring schemes. The mixture of type-I and type-II censoring schemes is known as the hybrid censoring scheme (HCS). The HCS was ﬁrst introduced by [1] and it becomes quite popular in reliability and life testing experiments. [2] gave details and additional references on some of the statistical inferences and applications for the exponential distribution with HCS. [1]introduced the type-I HCS in which the experimental time is T ∗ = min{x m:n , T }for a pre-ﬁxed value of T. The main disadvantage of type-I HCS is that most of the inferential results need to be developed in this case under the condition that the number of observed failures is at least one; moreover, there may be very few failures occurring up to the pre-ﬁxed time T which results in the estimator(s) of the model parameter(s) having low efﬁciency. For this reason, [3] introduced an alternative HCS that would terminate the experiment at the random time T ∗ = max{x m:n , T }. This HCS is called type-II hybrid censoring scheme (type-II HCS), and it has the advantage of guaranteeing at least m failures to be observed by the end of the experiment. If m failures occur before time T , then the experiment would continue up to time T which may end up yielding possibly more than m failures in the data. On the other hand, if the m−th failure does not occur before time T , then the experiment would continue until the time when the mth failure occurs in which case we would observe exactly m failures in the data.[4] combined type-I HCS and type-II HCS schemes and introduced the so-called uniﬁed HCS.[5] give detailed description on hybrid and adaptive censoring schemes, inferential methods and point out their advantages and ∗ Corresponding author e-mail: nashwa mohamed@science.suez.edu.eg c  2020 NSP Natural Sciences Publishing Cor.