Let {Xn ,n=>1} be a strictly stationary sequence of negatively associated random variables, with common distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) for fixed $K /in N$ based on kernel type estimators. We introduce asymptotic normality and properties and moments. From these we derive the optimal bandwidth...

Rail irregularity is one of the most effective factors in train derailment. theste irregularities have generally random distribution that are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probabiliy densities and zero mean values. The quality of irregularities, their distribution along the rails and wagon speed are the main factors for train derailment ...

The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary...

BACKGROUND The age distribution and remaining lifespan distribution are identical in stationary populations. The life table survival function is proportional to the age distribution in stationary populations. OBJECTIVE We provide an alternative interpretation of the life table when viewed by remaining years of life. CONCLUSIONS The functions describing the mortality of birth cohorts over ag...