Bayesian Inference for Mean of the Lognormal Distribution

Lognormal distribution has wide applications in the analysis of failure time data, stock prices and rainfall. In this paper we derive Bayes estimator and credible regions for the mean of the lognormal distribution. We compare the coverage probability and length of the Bayes credible interval with the confidence interval obtained from the maximum likelihood estimator of the log location and scale parameters. The procedure is illustrated using the failure time data of locomotive control and stock price. ognormal distribution has support on the positive part of the real line. It is right skewed and is widely applicable when normal distribution does not fit well to the data. It is used in the analysis of failure time data, stock market data and in the analysis of rainfall data. The commonly used procedure in this area is to take log transformation and use the technique developed for normal models. The mean and variance of the lognormal distribution are not invariant under distributional transformation. Therefore it is necessary to develop estimators and confidence intervals for the mean and variance of the lognormal distribution. In applied research coefficient of variation (C.V) is widely used as a measure of variability than the standard deviation. The reason for this is that C.V is unitless and facilitates easy interpretation. Zellner (1971) initiated Bayesian inference for lognormal distribution. He considered Bayes estimator for the mean and median of the lognormal distribution. He observed that Bayes estimator for mean of the lognormal distribution does not exist and he obtained improved estimators of mean and median of the distribution. He