Gordon Simons

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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. * Research(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)
General linear combinations of independent winnings in generalized St. Petersburg games are interpreted as individual gains that result from pooling strategies of different cooperative players. A weak law of large numbers is proved for all such combinations, along with some almost sure results for the smallest and largest accumulation points, and a(More)
We consider a binary symmetric channel where the input, modeled as an innnite sequence of bits, is distorted by a Bernoulli noise. In 8], a consistent estimator of the distortion, i.e., of the probability that a single bit is changed, is described under the basic assumption that the complexity of the input is nite. Here, we deal with two shortcomings: 1.(More)
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)
In the last century, Desire Andre obtained many remarkable properties of the numbers of alternating permutations, linking them to trigonometric functions among other things. By considering the probability that a random permutation is alternating and that a random sequence (from a uniform distribution) is alternating, and by conditioning on the first element(More)
Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables. The class of applicable distributions, herein described, extends beyond that for sample(More)
A random vector is said to have a I-symmetric distribution if its characteristic function is of the form ¢(Itll + ••• + Itnl). I-symmetric distributions are characterized through representations of the admissible functions ¢ and through stochastic representations of the random vectors, and some of their properties are studied. AMS 1970 Subject(More)