Nonparametric procedures are proposed for testing exponentiality against several new aging classes of life distributions. The main idea is to test if the lifetime of a system, whose failure time has occurred in between visits, belongs to some alternative new aging classes of life distribution....

An interesting recent result of [5], Ann. Probability 5, 595-600) is investigated further. Rates of convergence in the conditioned central limit theorem are developed for partial sums and maximum partial sums, with positive mean and zero mean separately, of sequences of independent identically...

Hollander, Park and Proschan (1986) proposed a test of new is better than used of a specified age. It is based on large sample normality of the test statistic. There is, however, no study in the literature on its actual size for small and moderate sample sizes. To shed some lights on this, the...

For a sequence of strictly stationary uniform or strong mixing we estimate the mean residual time of the marginal distribution from the first n observations. Under appropriate conditions it is shown that the estimate converges weakly to a well-defined Gaussian process even when the sample size...

Let X1,...,Xn be a random sample from a distribution function F. Let Fn(x)=(1/n)[summation operator]i=1nI(Xi[less-than-or-equals, slant]x) denote the corresponding empirical distribution function. The empirical process is defined by In this note, upper bounds are found for E(Dn) and for E(etDn),...