The predictive-sequential goodness-of-fit approach: a study of the exponential distribution case

Abstract

The predictive-sequential prequential approach is often used to measure the predictive quality of reliability-growth models eg: software-reliability models. Many practitioners use this approach as a goodness-of-fit test whereas no theoretical results justify such a use. This paper presents a theoretical study of the prequential approach in the case of the exponential distribution which is used in many reliability-growth models. We show that the prequential approach leads to a new goodness-of-fit test for the exponential distribution with unknown scale parameter. Monte Carlo simulations are used to compare the power of the prequential test to the standard exponentiality test. The obtained mathematical derivations represent a first step in the theoretical study of the prequential approach as used for validating and comparing reliability-growth models

Keywords:

• Prequential approach
• sequential estimation
• Kolmogorov-Smirnov distance and distribution
• Empirical distribution function
• Relibility-growth models
• u-plot