In this paper, the maximum likelihood and Bayesian estimations are developed based on an ordered pooled sample from two independent samples of record values from the left truncated exponential distribution. The Bayesian estimation for the unknown parameters is discussed using different loss functions. Also, the maximum likelihood and the Bayesian estimators of the corresponding reliability and pth quantile functions are calculated. The problem of predicting the record values from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.
Mohie El-Din, Mostafa; Abdel-Aty, Yahia; Shafay, Ahmed; and Nagy, Magdy
"Bayesian Inference for The Left Truncated Exponential Distribution based on Ordered Pooled Sample of Records,"
Journal of Statistics Applications & Probability: Vol. 4
, Article 1.
Available at: https://dc.naturalspublishing.com/jsap/vol4/iss1/1