Power Analysis of the Likelihood Ratio Test for Exponential Populations

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Transactions of the Nigerian Association of Mathematical Physics (Trans. of NAMP)


The statistical power of the likelihood ratio (LR) test for testing the parameter (λ) of the exponential distribution under different parameter considerations and sample sizes was investigated. Results from Monte Carlo studies showed that the power of the test is highly sensitive to the size of λ_0∈λ under H0 and λ_1∈λ under H1 from the parameter space λ being tested. As the values of both λ_0 and λ_1 progressively increase, more samples would be required before a small shift between them could be detected with appreciable power, even with equal effect sizes |λ_0-λ_1 | over various sizes of λ_0 and λ_1. However, the sample size required to attain a reasonable power by the test reduces as the value of the parameter ratio λ_0/λ_1 decreases with λ_0<λ_1. Further results indicated that fewer samples would be required by the test to achieve appreciable power as the chosen size α level increases. Empirical illustrations are provided to validate the results from Monte Carlo experiments.



Likelihood ratio test, Exponential distribution, Effect sizes, Statistical power