On a Less Cumbersome Method of Estimation of Parameters of Type III Generalized Logistic Distribution by Order Statistics

Abstract

In this work we have derived appropriate U-statistics from a sample of any size exceeding a specified integer to estimate the location and scale parameters of Type III generalized logistic distribution without the knowledge or by evaluation of the means, variances and co-variances of order statistics of an equivalent sample size arising from the corresponding standard form of distribution. The exact variances and the asymptotic variances of the estimators have been obtained. The efficiency of the obtained estimators relative to some of the standard estimators have been also obtained. An illustration describing the betterness of U-statistics estimation method over the classical maximum-likelihood method is also given.

Keywords

• Best linear unbiased estimators
• Beta-logistic distribution
• Max- imum -likelihood estimators
• Moment estimators
• Gini's mean dierence
• Type III generalized logistic distribution
• U-statistics