A comparison of methods of estimation of parameters of Tukey's gh family of distributions

The gh family of distributions proposed by Tukey (1977) based on a transformation of the standard normal variable does not have any explicit mathematical form. Thus the study of this distribution requires extensive numerical computations. In this paper we study the numerical methods of estimating the parameters g and h. We compare the three methods namely quantile method, method of moments and maximum likelihood method by using simulation technique. We have found that maximum likelihood method is more efficient than the other two methods though it requires much more computational load.