## On Empirical Likelihood Ratio Test for Equality of Means

### by Aruna K. Rao and Aparna U.

**Abstract:**
In this paper, empirical likelihood ratio test is proposed for equality of means of two distributions. Simulation is carried out to check the adequacy of the chi-square approximation with one degree of freedom and F approximation with (1, ) degrees of freedom where m and n denote the sample sizes, to the null distribution of the test statistic. The proposed test is compared to the t-test and the Wilcoxon-Mann-Whitney test when the variances of the two populations are unknown but equal. The simulation results indicate that the empirical likelihood ratio test has marginally smaller power compared to the t-test when the underlying distribution is normal. The empirical likelihood ratio test emerges as the best when the distributions are logistic, uniform, log-normal and gamma.
**Key Words: **
Empirical likelihood ratio test, t-test, Wilcoxon-Mann-Whitney test, type I error rate, power comparison

**Authors:**

Aruna K. Rao, , arunaraomu@gmail.com

Aparna U

**Editor:**
Abd-Elfattah A. M., a_afattah@hotmail.com On Empirical Likelihood Ratio Test for Equality of Means
by Aruna K. Rao and Aparna U.

## On Empirical Likelihood Ratio Test for Equality of Means

### by Aruna K. Rao and Aparna U.

**Abstract:**
In this paper, empirical likelihood ratio test is proposed for equality of means of two distributions. Simulation is carried out to check the adequacy of the chi-square approximation with one degree of freedom and F approximation with (1, ) degrees of freedom where m and n denote the sample sizes, to the null distribution of the test statistic. The proposed test is compared to the t-test and the Wilcoxon-Mann-Whitney test when the variances of the two populations are unknown but equal. The simulation results indicate that the empirical likelihood ratio test has marginally smaller power compared to the t-test when the underlying distribution is normal. The empirical likelihood ratio test emerges as the best when the distributions are logistic, uniform, log-normal and gamma.
**Key Words: **
Empirical likelihood ratio test, t-test, Wilcoxon-Mann-Whitney test, type I error rate, power comparison

**Authors:**

Aruna K. Rao, , arunaraomu@gmail.com

Aparna U

**Editor:**
Abd-Elfattah A. M., a_afattah@hotmail.com

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