Inference for the shape parameter of lognormal distribution in presence of fuzzy data

Abstract

Traditional Statistical analysis of lognormal distribution have been proposed for precisely defined crisp data.
But there are many other situations in which measurement results from
continuous quantities are not precise numbers but more or less fuzzy. This article presents the statistical inference on the shape parameter of lognormal distribution involving experiment whose observations are described in terms of fuzzy data. The maximum likelihood procedure are developed for estimating the unknown parameter. Asymptotic distribution of maximum likelihood estimator is used to construct approximate confidence interval. Also, Bayes estimate and the corresponding highest posterior density credible interval of the unknown parameter are obtained by using Markov Chain Monte Carlo technique. In
addition, we describe an estimation method based on moments of
lognormal distribution. Extensive simulations are performed to compare the performances of the different proposed methods.