Inferential Survival Analysis for Type II Censored Truncated Exponential Topp Leone Exponential Distribution with Application to Engineering Data

This study focuses on estimating the unknown parameters of the truncated exponential Topp-Leon distribution using a type II scheme. We estimate the unknown parameters, survival, and hazard functions using maximum likelihood estimation methods. Additionally, we derive the approximate variance covariance matrix and asymptotic confidence intervals. Furthermore, we compute Bayesian estimates of the unknown parameters under squared error and linear loss functions. To generate samples from the posterior density functions, we use the Metropolies-Hastings algorithm. We demonstrate the effectiveness of the proposed distribution by applying it to two data sets: Monte Carlo simulation and real data set. Our results show that the proposed distribution provides accurate estimates of the unknown parameters and performs well in fitting the data. Our findings also indicate that Bayesian estimation can provide more precise estimates with narrower confidence intervals compared to maximum likelihood estimation method. In summary, the study provides a comprehensive analysis of the estimation of the unknown parameters for the truncated exponential Topp-Leone distribution using a type II scheme. Also, the results demonstrate the potential of this distribution in modeling real data and the usefulness of both maximum likelihood and Bayesian estimation methods in obtaining accurate parameter estimates

Parameters and Reliability Estimation of Left Truncated Gumbel Distribution under Progressive Type II Censored with Repairable Mechanical Equipment Data

The estimation of two parameters of the left truncated Gumbel distribution using the progressive type II censoring scheme is discussed. We first derived the maximum likelihood estimators of the unknown parameters. The approximate asymptotic variance-covariance matrix and approximate confidence intervals based on the asymptotic normality of the classical estimators are calculated. Also, the survival and hazard functions are derived. Further, the delta method is used to construct approximate confidence intervals for survival and hazard functions. Using the left truncated normal prior for the location parameter and an inverted gamma prior for the scale parameter, several Bayes estimates based on squared error and general entropy loss functions are computed. Bayes estimators of the unknown parameters cannot be calculated in closed forms. Markov chain Monte Carlo method, namely Metropolis-Hastings algorithm, has been used to derive the approximate Bayes estimates. Also, the credible intervals are constructed by using Markov chain Monte Carlo samples. Finally, The Monte Carlo simulation study compares the performances among various estimates in terms of their root mean squared errors, mean absolute biased, average confidence lengths, and coverage probabilities under different sets of values of sample sizes, number of failures and censoring schemes. Moreover, a numerical example with a real data set and Markov chain Monte Carlo data sets are tackled to highlight the importance of the proposed methods. Bayes Markov chain Monte Carlo estimates have performed better than those obtained based on the likelihood function