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In this paper, the parameters of the two-parameter exponentiated log-logistic distribution based on a complete sample are estimated using the Markov chain Monte Carlo (MCMC) method. In order to perform full Bayesian analysis of the two-parameter exponentiated log-logistic distribution, the procedures are developed using the MCMC simulation method in Open BUGS, established software. The researcher has obtained the Bayes estimates of the parameters and their probability intervals are presented. The researcher has also discussed the estimation of the reliability function. For illustration under independent gamma priors, the real data set is considered.

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A new distribution having three parameters using half Cauchy family of distribution named half Cauchy modified exponential distribution is deliberated and studied in this work. Its mathematical and statistical properties are examined. Model parameters of novel distribution are evaluated using least-square, maximum likelihood and Cramer-Von-Mises estimations approaches. R programming software is applied to carry out all of the calculations. To evaluate the new distribution's application and goodness-of-fit test, an actual data set is studied for illustration. The suggested new distribution is performed better as compared to some existing distributions.