Characteristic function and Laplace transform‐based tests for exponentiality in the presence of random right censoring

Abstract

In this paper, the composite hypothesis that lifetimes follow an exponential distribution is tested based on observed randomly right censored data. Testing this hypothesis is complicated by the presence of this censoring, due to the fact that not all lifetimes are observed. To account for this complication, we propose modifications to tests based on the empirical characteristic function and Laplace transform. In the full sample case, these empirical functions can be expressed as integrals with respect to the empirical distribution function of the lifetimes. We propose replacing this estimate of the distribution function by the Kaplan–Meier estimate. The resulting test statistics can be expressed in easily calculable forms in terms of summations of functionals of the observed data. Additionally, a general framework for goodness‐of‐fit testing, in the presence of random right censoring, is outlined. A Monte Carlo study is performed, the results of which indicate that the newly modified tests generally outperform the existing tests. A practical application, concerning initial remission times of leukaemia patients, is discussed along with some concluding remarks and avenues for future research.

On a new class of tests for the Pareto distribution using Fourier methods

“…Some work in this regard has been done by Fernández and Rivera (2020), where they consider Kaplan‐Meier $$$ U $$$ and $$$ V $$$ statistics, and by Cuparić and Milošević (2022), where they derive asymptotic results for a new characterization based test for exponentiality in the presence of random right censored data. Further details regarding the development of tests for the censored exponential distribution can be found in Bothma et al (2021), while Bothma et al (2022) consider tests for the censored Weibull distribution. For results pertaining specifically to tests for the censored Pareto distribution, the interested reader is referred to Ndwandwe et al (2021).…”

Logistic or not Logistic?

“…One possibility is to estimate the expected value in (3) by estimating the law of the survival times by the well-known Kaplan-Meier estimate. Some work on this has been done in the case of testing for exponentiality (see, e.g., Cupari ć &Miloševi ć, 2022 andBothma, Allison, Cockeran, &Visagie, 2021).…”

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

“…Naturally, this modification will complicate some of the asymptotic derivations and might be an avenue for future research. Some work in this regard has been started by [32] as well as [33].…”