Exact Bahadur slope for combining independent tests for normal and logistic distributions

Combining independent tests of hypotheses is an important and popular statistical practice. Usually, data about a certain phenomena come from different sources in different times, so we want to combine these data to study these phenomena. Several combination methods were used to combine infinity independent tests. These methods are Fisher, logistic, sum of P-values and inverse normal for testing simple hypotheses against one-sided alternative. These methods are compared via the exact Bahadur slope (EBS). These non-parametric methods depend on the P-value of the individual tests combined.