Abstract
The exponentially modified Gaussian (EMG) distribution is adopted in many fields such as psychology, chromatographic peaks, and cell biology. In this article, we focus on the test for the parameters of the EMG distribution. The primary test statistic is the classical likelihood ratio. Although the EMG distribution is an asymmetric one, we proved that the logarithm of the likelihood ratio is asymptotically distributed as that is, the Wilks phenomenon. We employ Q–Q plots to illustrate the sample sizes needed for the asymptotic distribution as a good approximation to the null distribution of the loglikelihood ratio for different parameters. The available approximate distribution for the loglikelihood ratio is guaranteed by a relatively large sample size. Hence, when the sample size is small, the approximate distribution is inapplicable, since the EMG distribution is asymmetric. For the small sample size, we propose a parametric bootstrap algorithm, which is demonstrated to be successful by the simulation studies. An application of our method to a real data example shows that the test is satisfactory.
Published Version
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