Testing exponentiality of the residual life, based on dynamic Kullback-Leibler information

This paper proposes a test-of-fit for exponentiality of the residual life (TF-ERL) based on the estimated dynamic Kullback-Leibler information. TF-ERL applies when the exponential parameter is or is not specified under the null hypothesis. Asymptotic properties of TF-ERL are discussed. In particular, the TF-ERL is shown to be a statistically consistent test of the null hypothesis for all alternatives. Small-sample null tail probabilities are derived; critical values are tabulated; and its use is shown in an example. Monte-Carlo simulation is used to compute the power of TF-ERL under various alternatives; it performs well in terms of its power.