Confidence interval estimation of the location and scale parameters of the logistic distribution using pivotal method

Abstract

Different confidence intervals (CI) will be constructed for the location and scale parameters of the logistic distribution by assuming that one of them is known. The maximum likelihood estimator and several different pivots will be used to construct different CI for the logistic parameters, using simple random sampling (SRS) and ranked set sampling (RSS). They will be compared via their expected lengths and the standard errors of their lengths using computer simulation. The CIs based on the RSS are found to be more efficient, i.e. having shorter expected lengths and smaller standard errors than their competitors based on the SRS.

Keywords:

• efficiency
• expected length
• maximum likelihood estimator
• pivotal method
• ranked set sampling
• simple random sampling

Acknowledgements

This work was supported by King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia under the fast track project # FT/2006-21.