Asymptotics for continuous lifetime distributions with polynomial failure rate with an application in reliability

This paper is a continuation of work reported by Csenki (2011 ), where the coefficients of a polynomial failure rate function of a continuous lifetime distribution were expressed in terms of derivatives of the Laplace transform of the distribution at the origin. Here it is shown that these expressions are asymptotically normal. The main tool employed is the Delta Method in conjunction with the Central Limit Theorem. The finding is used to derive asymptotic confidence intervals and tests for the coefficients. The suggested calculations are carried out for a set of bus failure data from the literature.