classical and bayesian estimation of the reliability function for the inverse lindley distribution based on lower record statistics

The reliability function‎, ‎or the survival function at a specified time t‎, ‎denotes the proportion of products that remain operational beyond time t and continue to function‎. ‎this interpretation underscores the pivotal role of the survival function and its estimation in understanding lifetime phenomena‎. ‎this paper explores the estimation of the survival function for the inverse lindley distribution based on lower records‎. ‎the estimation techniques encompass maximum likelihood and bootstrap methods‎. ‎furthermore‎, ‎bayesian approaches employing metropolis-hastings and importance sampling algorithms are employed‎. ‎in addition to deriving approximate confidence intervals using the delta method and percentile bootstrap intervals for the survival function‎, ‎chen and shao's shortest width credible intervals are also determined‎. ‎a comprehensive simulation study is presented to assess the effectiveness of both point and interval estimators‎. finally‎, ‎an application of the results is given to a real data set.