Data Dependent Cells Chi‐Square Test With Recurrent Events

We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F . In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q ‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator . Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.