On the Parameter Estimation of Johnson’s System of Distribution

Abstract

The estimation of the two shape parameters of the Johnson’s System of Distributions (JSD) via the Maximum
Likelihood Estimation (MLE) method has received considerable attention in the literature. This paper is a research
expounded in this direction, albeit via the methods of least squares and moment. The location and the scale parameters of the JSD are obtained in closed form under certain regularity conditions. In order to circumvent the computational agony in the estimation procedure, a third shape parameter is introduced by means of the pivotal quantity method. The utility of the method is illustrated using both simulated and real-life data.