Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative efficiency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test b...

U -statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener–Itô chaos expansion. In the second half we obtain more explicit results for a system of U -statistics of some parametric models in stochastic geometry. In the ...

The problem of sample size determination based on three commonly used non-parametric rank based tests, namely, one-sample Wilcoxon's rank sum test, two-sample's Wilcoxon's rank sum test, and the rank-based test for independence is studied. Explicit formulas for variabilities of the test statistics under the alternative hypotheses are derived. Consequently, close forms of power functions of thes...

In this paper we analyze the quantum uncertainties and the photon statistics in the interaction between the two modes of radiation by treating them as coupled harmonic oscillator with the motivation of controlling quantum properties of one light beam by another. Under the rotating wave approximation (RWA) we show that if initially one of the modes is coherent and the other one squeezed, then th...