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In this article, the author focus on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach of two sample compound Poisson process under infinite second moment. It is shown that the log empirical likelihood ratio statistic for the difference of two population means converges in distribution toasThe simulation results show that the empirical likelihood ratio method is applicable under infinite second moment.

Empirical likelihood ratio for two-sample compound Poisson processes under infinite second moment