Consider n players whose ‘‘scores’’ are independent and identically distributed values fXigi 1⁄4 1 from some discrete distribution F. We pay special attention to the cases where (i) F is geometric with parameter p-0 and (ii) F is uniform on f1;2; . . . ;Ng; the latter case clearly corresponds to the classical occupancy problem. The quantities of interest to us are, first, the U-statistic W whic...

We give a derivation of the frequentist predictive distribution for a simple Poisson model, show how this simple model may be adapted to fit a claim count triangle, and demonstrate how the predictive distribution of aggregates of future claim counts may be computed for the adapted model. Quantiles and prediction intervals are readily obtained. Quasi-Poisson models for incremental paid losses ar...

Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution. We are able to derive strong constraints on such deviations by using the detailed helioseismic information of the solar structure. If a small deviation is parameterized with a factor exp{−δ(E/kT) 2 ...

New uniform asymptotic approximations with error bounds are derived for a generalized total variation distance of Poisson approximations to the Poisson-binomial distribution. The method of proof is also applicable to other Poisson approximation problems. MSC 2000 Subject Classifications: Primary 62E17; secondary 60C05.

We briefly describe sensitivity analysis methods for simulation via stochastic intensities and give applications on derivative estimation of event averages. We consider a process depending on a parameter and an event-counting process and obtain expressions for the derivatives of the expected number of events occurring while the process is in a given set. The necessary assumptions of these expre...

Consider random regular graphs of order n and degree d = d(n) ≥ 3. Let g = g(n) ≥ 3 satisfy (d− 1)2g−1 = o(n). Then the number of cycles of lengths up to g have a distribution similar to that of independent Poisson variables. In particular, we find the asymptotic probability that there are no cycles with sizes in a given set, including the probability that the girth is greater than g. A corresp...

This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in Rn (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of volume preserving diffeomorphism group. This is interesting and nontrivial because in Eulerian representation, the time t maps need not be C from th...

Boltzmann equation was successfully used for transport description and modeling in conventional semiconductor devices from the early development of semiconductor technology. Due to a rapid down scaling of transistor dimensions, with the 90 nm technology node being already industrially implemented, quantum effects becomes more pronounced, and the question of going beyond the semiclassical approa...

As know, a ballistic MOS-Like carbon nanotube FET can be simulated by using a self-consistent procedure between the charge and the Poisson equations. Because of the integral form of the charge equation, this model cannot be implemented in the commercially available circuit simulators, such as SPICE. In this paper, we propose an analytical solution for estimating the charge equation, so that the...

We present an approach for solving the Boltzmann equation based on the explicit construction of the Green’s functions. The Green’s function approach has been useful for the study of nonlinear interior waves and the boundary waves. In this Part I we study the Green’s functions for the initial and initial-boundary value problems. In the forthcoming Part II, we will study the general solutions of ...