New goodness-of-fit test for exponentiality based on a conditional moment characterisation

Abstract

The exponential distribution plays a key role in the practical application of reliability theory, survival analysis, engineering and queuing theory. These applications often rely on the underlying assumption that the observed data originate from an exponential distribution. In this paper, two new tests for exponentiality are proposed, which are based on a conditional second moment characterisation. The proposed tests are compared to various established tests for exponentiality by means of a simulation study where it is found that the new tests perform favourably relative to the existing tests. The tests are also applied to real-world data sets with independent and identically distributed data as well as to simulated data from a Cox proportional hazards model, to determine whether the residuals obtained from the fitted model follow a standard exponential distribution.