Likelihood Ratio and Other Tests

The likelihood ratio tests provide useful methodologies. This general approach to construct test procedures for composite null and alternative hypotheses was developed by Neyman and Pearson. This chapter introduces likelihood ratio (LR) tests for the mean and variance of a normal population. It discusses LR tests for comparing the means and variances of two independent normal populations. The authors focus on a single normal population and some LR tests associated with it. They focus on two independent normal populations and some associated likelihood ratio tests. The authors have discussed LR tests to check the equality of means of two independent normal populations. In some situations, however, the two normal populations may be dependent.