期刊名称：Pakistan Journal of Statistics and Operation Research
印刷版ISSN：2220-5810
出版年度：2016
卷号：12
期号：1
页码：89-99
DOI：10.18187/pjsor.v12i1.1084
语种：English
出版社：College of Statistical and Actuarial Sciences
摘要：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.
其他摘要：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.
关键词：Fuzzy data analysis; lognormal distribution; Maximum likelihood principle; Bayesian estimation; Credible interval
