On the parameter estimation for quantile class Ⅰ distribution

Due to its great flexibility in tail heaviness at both sides,the Quantile Class Ⅰ distribution has the capability to fit many data sets that the classical distributions cannot handle.Ever since it is proposed,it has been successfully used in the empirical studies in the Chinese Stock market,the International stock markets,foreign exchange market,American electricity markets and turbulence data in hydrodynamics.Since it is a brand new distribution class,many statistical issues,such as parameter estimation,hypothesis testing,remain unstudied or at least unsystematic studied.With the increasing of the applications,it becomes more and more important to provide a reliable method to do the standard statistical analysis.We have deeply investigated the performance of the Maximum estimation method working with the Quantile Class Ⅰ distribution.We have proved the consistency and have built the related central limit theorem of the MLE.