On the xgamma k-record values and associated inference

The xgamma distribution was first introduced by Sen et al. [1] as an alternative distribution to the exponential model. The xgamma distribution exhibits a bathtub-shaped hazard rate function, so it is suitable for many lifetime phenomena. In this paper, we consider the upper k-record values from the xgamma distribution. We obtain exact explicit expressions for the moments of k-record values. We compute the means, variances, and covariances of the upper k-records. Using these computed values, we can find the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale parameters of the xgamma model. In addition, we work on the prediction of a future k-record value. We find the best linear unbiased predictor (BLUP) and the best linear invariant predictor (BLIP) of a future k-record value. Another linear predictor is also discussed. A simulation study is performed to assess the proposed estimators and predictors. We also present a real data example in order to illustrate the application of the theoretical results of the paper. At the end of the paper, we will provide several concluding remarks.