A Selection Procedure for Selecting the Least Increasing Failure Rate Average Distribution

For k independent absolutely continuous increasing failure rate average (IFRA) life distributions F_i, i = 1, 2, …, k, Link (1989 Link, W.A. (1989). Testing for exponentiality against monotone failure rate average alternatives. Commun. Statist. Theor. Meth. 18(8): 3009–3017.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) considered a measure of departure of against monotone failure rate average alternatives. In this paper, we use the measure defined by Link for detection of IFRA-ness of life distribution F_i. A two-stage selection procedure to select the least IFRA distribution is proposed. This selection procedure is based on a U-statistic which is an estimator of the measure and can be implemented even when the IFRA life distributions belong to different families. The applications of this procedure are discussed for some well known distributions.