Shanker [4] has discussed its various mathematical and statistical properties including its shape for different values of its parameter, moment generating function, moments, skewness, kurtosis, hazard rate function, mean residual life function, stochastic orderings, mean deviations, Bonferroni and Lorenz curves, amongst others. Further, Shanker [4] has also discussed the estimation of its param...

In this paper we propose a new statistical model for multi-scale traffic, and present an exact queueing analysis for the model. The model is based on the central moments and the marginal distributions of the cumulative traffic loads in different time scales. Only the first two moments are needed to characterize the traffic process, which greatly simplifies the representation and estimation. The...

There are a large number of different approaches to vehicle tracking currently available. In this report we look at different problems faced when tracking vehicles, such as background subtraction and vehicle recognition, and look at possible solutions to these. We present a layered approach to vehicle tracking, which includes the use of background subtraction based on a statistical colour model...

We consider scalar hyperbolic conservation laws in several (d ≥ 1) spatial dimensions with stochastic initial data. We prove existence and uniqueness of a random-entropy solution and show existence of statistical moments of any order k of this random entropy solution. We present a class of numerical schemes of multi-level Monte Carlo Finite Volume (MLMC-FVM) type for the approximation of random...

The recently introduced correntropy function is an interesting and useful similarity measure between two random variables which has found myriad applications in signal processing. A series expansion for correntropy in terms of higher-order moments of the difference between the two random variables has been used to try to explain its statistical properties for uses such as deconvolution. We exam...

The continuity of capacitor voltages and inductor currents, well-known from the deterministic case, cannot be directly applied if the initial conditions are random. In this paper, new continuity relations for probability densities, mean values, correlation and covariance functions of the state variables are introduced. These continuity relations can be used for a global characterization of rand...

A simple scheme is presented for modifying geometric moments to use geodesic distances. This provides a set of global shape descriptors that are invariant to bending as well as rotation, translation and scale.

Abstract. This paper considers the timeand space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L1-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of...