the parameter space or parameters with a zero variance) is relatively high in smaller samples, and even higher when combined with large and small $\gamma$ values. These cases are eliminated from the frequentist calculations. The five tables in Appendix 2 of the Supplementary Web Materials give a summary of results of the simulation study. In each cell, we compute two numbers: the proportion of empirical coverages within 0.01 of the nominal coverage and the proportion of empirical coverages above -0.02 of the nominal coverage. The latter summary carries out more value than the former one. The findings for the ETCP criterion are summarized as follows.

-   For $\Delta=0$, Bayesian HPD intervals perform similarly for moderate and large sample sizes ($m=50, 100$) and the proportions of coverages above -0.02 of the nominal coverage are close to 100% for $\lambda_0,\lambda_1$ and $\Delta$. This finding actually holds true for $\Delta\leq0.4$.

-   Wald FCIs perform poorly for estimating $\lambda_0$ and $\lambda_1$ when $m=10, 25$ and $\Delta\leq0.3$.

-   Overall, in terms of coverage probability, the uniform distribution seems to perform better than the other methods when $\Delta
    \leq
    0.5$. When $\Delta\geq0.6$, Jeffreys’ prior and the reference prior perform better when estimating $\lambda_0$, $\lambda_1$ and $\Delta$.

