Exponentiality versus generalized Pareto — a resistant and robust test

Abstract

Using resistant and robust methods we propose the statistic Tn = (FU −M)/(M −FL) for testing exponentiality versus generalized Pareto, where FU , FL and M are, respectively, the upper and lower fourths and the median of a random sample of size n. The statistic Tn is based on the statistic Vn = (Xn:n−M)/(M −X1:n) used by Gomes (1982) to discriminate extremal models in a similar context but with a higher breakdown point. The simulated power of Tn is compared with the simulated power of Un =Xn:n/M and Vn, which can also be used to test the exponential behaviour of the sample data. Although we observe that the power of Tn is lower than the power of Un and Vn, we show that the performance of the first test is better than the performance of the two other tests when compared to broadened situations and mixtures commonly used to evaluate resistance and robustness.