Efficient Confidence Interval Mean Estimation for Commonly-Used Statistical Distribution Modeling Earth System Sciences- Sameer Verma

by Sameer Verma and Ashok Sahai.

Abstract: Log-normal distribution has now emerged as a popular distribution in modeling various problems in the areas of various sciences, including most conspicuously the bio-medical field. In the context of the earth system sciences, we do find in literature the mention of this distribution being tried for modeling since late 40's. However, it is since the last decade that the log-normal distribution has been quite convincingly accepted for modeling in various areas of earth system sciences. The interest of the contemporary earth system sciences' researchers in this distribution has been increasingly evidenced since the dawn of the current millennium, very conspicuously. The parametric estimation problem for the log-normal distribution has been tried by statisticians and the biomedical researchers in particular in the recent past. As Confidence Interval (C.I.) estimation is most relevant in the decision-theoretic setup of statistical modeling, this paper addresses the efficient 'C.I.' estimation problem for the mean of the log-normal distribution. The relative efficiency of the proposed C.I. estimates, as compared to the currently-used C.I. has been illustrated through a simulation study in the paper.

Key Words: Log-Normal population mean, confidence interval, simulation study

Sameer Verma, sverma@sfsu.edu
Ashok Sahai, sahai.ashok@gmail.com

Editor: Ahmed H. Youssef, sahai.ashok@gmail.com Editor: Ahmed H. Youssef; ahyoussef@hotmail.com

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