Moments inequalities of aging families of distributions with hypotheses testing applications

Nonparametric families of aging distributions have been the subject of investigation for more than three decades. Both probabilistic and statistical properties of these distributions were studied for such families as increasing failure rate , new better than used , new better than used in expectation , and harmonic new better than used in expectation . In the present work, moments inequalities are derived for the above-mentioned four families that demonstrate that if the mean life is finite for any of them then all higher-order moments exist. Next, based on these inequalities, new testing procedures for exponentiality against any one of the above classes are introduced and studied showing that they are simpler than most earlier ones and hold high relative efficiency for some commonly used alternatives. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: primary: 60E15, 62G15; secondary: 62N05