A Laplace-transform based goodness-of-fit test for exponentiality under Type-II censoring

Abstract

We propose a Laplace-transform-based goodness-of-fit test for the exponential distribution under Type-II censored data. The test is constructed using the conditional empirical Laplace transform of observed failures and compares it with the theoretical Laplace transform under exponentiality. We derive the asymptotic properties of the proposed statistic under the null hypothesis, establish its consistency against fixed alternatives, and characterize its behavior under contiguous local alternatives. Since the null distribution is analytically intractable, a parametric bootstrap procedure is used for calibration. Monte Carlo simulations show that the proposed test maintains satisfactory Type-I error control and generally outperforms several classical competing methods across a wide range of alternatives, particularly under skewed and heavy-tailed models. A real data application illustrates its practical usefulness under moderate sample sizes and censoring.