Finite-sample critical values for goodness-of-fit tests under the exponential distribution.

What the paper says

Goodness-of-fit tests based on the likelihood ratio are widely used to assess whether a given probability distribution adequately describes observed data.However, certain likelihood ratio-based tests do not have known asymptotic distributions, making it necessary to rely on pre-tabulated critical values obtained through Monte Carlo simulations.A major limitation of this approach is that practitioners must generate additional critical values via simulations for sample sizes not explicitly tabulated, which restricts the applicability of these tests in practice.This study addresses this limitation by developing asymptotic critical value functions for likelihood ratio-based goodness-of-fit tests under the exponential distribution.The proposed methodology employs response surface analysis to express simulated critical values as functions of sample size, enabling rapid computation of finite-sample critical values without requiring extensive simulations.The response surface regressions are estimated using median regression, ensuring robustness to outliers and heteroskedasticity.Extensive Monte Carlo experiments demonstrate that the estimated asymptotic critical value functions provide highly accurate test sizes across a wide range of sample sizes.