The Randomized Estimate and Vertical Density Representation test for the generalized Pareto distributionbased on upper record values

• 1、College of Applied Science, Beijing University of Technology, Beijing 100124

Abstract：In this paper parameter generalized Pareto distribution(GPD) is considered.The problem of estimating parameters of the GPD is studiedwhen the data available are upper record values.We develop Randomized Estimate (RE) for the location and scaleparameters.The Randomized Estimates for the parameters are derived from Fisher's fiducial inference.It sees parameter as constant, but the parameter can be estimated by random variable.RE not only obeys classical statistics, but also agrees to fiducial inference that parameter can be defined as random variable.In addition, new parameter tests, called Vertical Density Representation (VDR), are studied for the location and scale parameters of the GPD basing on the upper records.The superiority of the proposed method is thatthe distributions of pivots are exact distribution instead of approximate distribution.The combination of the RE and VDR technique is applied to parameter hypothesis test.Simulation studies show that simulated level of hypothesis tests forthe parameters are close to a significant level.The advantage of this simulated P value method is needless to simulate the percentage points of test statistics.As an universal tool,the VDR test could be applied to solve statistical inference.

keywords： Statistics, Randomized Estimate, Vertical Density Representation test,Hypothesis test, Power

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