In this note, we consider a question of Móri regarding estimating the deviation of the kth terms of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [0, 1]. An optimal bound for distributions on finite support is obtained. Properties of Chebyshev polynomials are employed.

The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous distributions. However, this is no longer true for discrete distributions or sampleswith ties.We show that the definition of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic properties of sample q...

the problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including binomial negative binomial discrete weibull and etc., is considered. we give necessary and sufficient conditions for which the bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function. for s...

In this paper the two identical unit cold standby systems with single repairman has been discussed.The concept of inspection policy has also been introduced for detecting the kind of failures (major or minor) before the failed unit get repaired by some repair mechanism.The model has been design for the system to calculate the various important measures of reliability i.e MTSF, steady state avai...

Estimation of L norms of Fourier multipliers is known to be hard. It is usually connected to some interesting types of PDE, see several such PDE for several Fourier multipliers on the line in a recent paper of Kalton and Verbitsky [13]. Sometimes, but much more rarely, one can establish sharp L estimates for Fourier multipliers in several variables. Riesz transforms are examples of success. The...

We apply a simple linearization, well known in solid state physics, to approximate the evolution at early times of cosmological N-body simulations of gravity. In the limit that the initial perturbations, applied to an infinite perfect lattice, are at wavelengths much greater than the lattice spacing l, the evolution is exactly that of a pressureless self-gravitating fluid treated in the analogo...