On the posterior distribution of location parameter of log-normal distribution

Bayesian estimation technique is widely used for estimation purposes due to its phenomenal performance in estimating the unknown parameter(s). in this study,bayesian estimation technique is employed to estimate the location parameter of log-normal distribution. two non-informative priors (uniform and jeffreys),two informative priors (normal and cauchy) and four loss functions are utilized for this purpose. prior predictive distributions are used to elicit the prior densities. the main purpose of this study is to search for a suitable prior and loss function for estimation of the location parameter of log-normal distribution. through simulation study,comparisons are made on the basis of the posterior variances,coefficients of skewness,ex-kurtosis and bayes risks. a real data of failure time is used to verify the simulation results. numerical results for cauchy prior and quadratics loss function have been obtained by solving the expressions numerically using the “quadrature” method in “mathematica 9”. � 2016 pakistan journal of statistics.