In this article the reliability estimation of the generalized half-normal distribution (GHN) is considered when data are subject to both left truncation and right censoring (LTRC). Since the EM-algorithm for the generalized gamma distribution (that includes GHN as a special case) based on LTRC data was developed in Balakrishnan and Mitra [Em-based likelihood inference for some lifetime distributions based on left truncated and right censored data and associated model discrimination; 2014, South African Statistical Journal, 48(2), 125–171], the maximum likelihood estimates, as well as asymptotic confidence intervals (CIs) and bootstrap CIs for the unknown parameters of GHN, are briefly discussed. For further study, we utilized a hierarchical Bayesian approach and proposed two sampling techniques, the Metropolis-Hastings algorithm and the slice sampler technique to carry out the Bayesian estimation procedure under squared error loss function, which can be easily extended to other loss function situations. In addition, the Bayesian prediction problem concerning the lifetime of a censored unit and the Bayesian estimates of the expected number of failures in a prefixed interval are investigated. Finally, some simulation studies are carried out to compare the performance of the proposed procedure with its competitor and data analysis of the electric power-transformers data is conducted to illustrate the purposes.
