The estimation and inference on the equal ratios of means to standard deviations of normal populations

This paper considers the estimation and the hypothesis testing on the equality of the ratios of the means to standard deviations of several normal populations with difference sample sizes. We propose an iterative algorithm to find the maximum likelihood estimates (MLEs) of the normal population means and standard deviations when the ratios of the means to the standard deviations are equal. A bootstrap method is introduced to determine the critical value in the likelihood ratio test. The simulation studies indicate that the proposed hypothesis testing performs well. Copyright Springer-Verlag Berlin Heidelberg 2015