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The theory of elliptically contoured distributions is presented in an unrestricted setting (without reference to moment restrictions or assumptions of absolute continuity). These distributions are defined parametrically through their characteristic functions, and then studied primarily through the use of stochastic representations which naturally follow… (More)

When k(x,Y) "<.is~a quasi-monotone function a.'1d the random variables X and Y have fixed distributions, it is sho1~ under some further mild conditions that Ek(X,Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions.

- Gordon Simons
- 2008

ABSTUCT The problem of optimally allocating partially effective, defensive weapons against randomly arriving enemy aircraft so that a bomber maximizes its probability of reaching its designated target is considered in the usual continuous-time context, and in a discrete-time context. The problem becomes that of determining the optimal number of missiles… (More)

Suppose you have u units of ammunition and want to destroy as many as possible of a sequence of attacking enemy aircraft. If you fire v = v(u), 0 ~ v ~ u, units of your ammunition at the first enemy, it survives with probability qv, where 0 < q < 1 is given, and then kills you. With the complementary probability, 1-qV, you destroy the aircraft and you live… (More)

- MATRIXGordon Simons, Gordon Simons
- 2007

It is shown for an n n symmetric positive deenite matrix T = (t i;j) with negative oo-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order 1=n 2

For an arbitrary point of a homogeneous Poisson point process in a d-dimen-siona! Euclidean space, consider the number of Poisson points that have that given point as their r-th nearest neighbor (r = 1,2,...). It is shown that as d tends to infinity, these nearest neighbor counts (r = 1,2,...) are tid asymptotically Poisson with mean 1. The proof relies on… (More)

- Gordon Simons
- 2008

A set of examples is described which suggests that members of a certain class of Markov processes have infinitely divisible limit distributions. A counter example rilles out such a possibility and raises the question of what further restrictions are required to guarantee infinitely divisible limits. Some related examples illustrate the same occurrence of… (More)