Comparison of loss functions for estimating the scale parameter of log-normal distribution using non-informative priors

The estimation of parameters of distributions is a core topic in the literature on Statistical methodology. Many Bayesian and classical approaches have been derived for estimating parameters. In this study, Bayesian estimation technique is adopted for the comparison of two non-informative priors and six loss functions to estimate the scale parameter of Log-Normal distribution assuming fixed values of location parameter. The main purpose of this study is to search for a suitable prior when no prior information is available and to look for an appropriate loss function for estimation of the scale 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. The simulation results are verified through a real data set of lung cancer patients.