| 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.In this paper, we have deeply investigated the performance of the Maximum estimation method working with the Quantile Class Ⅰ distribution. We have proved the consistency and asymptotic normality of the MLE. Building on these results, we also propose the theorems about hypothesis testing and confidence interval. In the end, we carry on the numerical simulation using Mat lab. When μ is known, the simulation results verify the corresponding theories. Further, we product numerical simulation when μ is unknown,and the estimators show that the MLEs for the entire parameters have good properties. |
