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71.
Shaul K. Bar-Lev Daoud Bshouty Peter Enis Gérard Letac I-Li Lu Donald Richards 《Journal of Theoretical Probability》1994,7(4):883-929
A natural exponential family (NEF)F in ? n ,n>1, is said to be diagonal if there existn functions,a 1,...,a n , on some intervals of ?, such that the covariance matrixV F (m) ofF has diagonal (a 1(m 1),...,a n (m n )), for allm=(m 1,...,m n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? k and ? n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? n , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? n , under what conditions is its projectionp(F) in ? k , underp(x 1,...,x n )∶=(x 1,...,x k ),k=1,...,n?1, still an NEF in ? k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV F (m 1,...,m n ) does not depend on (m k+1,...,m n ). 相似文献
72.
If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk
n
wherek
n+1
ck
n
then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG). 相似文献
73.
J. Neveu 《Stochastic Processes and their Applications》1985,19(2):237-258
Given a stationary stochastic continuous demand of service σ(θtω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes such that for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [Tn, Tn+1[ the demand of service accumulated during the proceding intervals [Tn?1, Tn[ and take a rest of fixed duration D. 相似文献
74.
75.
76.
Groshev gave a characterization of the union of domains of partial attraction of all Poisson laws in 1941. His classical condition is expressed by the underlying distribution function and disguises the role of the mean of the attracting distribution. In the present paper we start out from results of the recent probabilistic approach and derive characterizations for any fixed >0 in terms of the underlying quantile function. The approach identifies the portion of the sample that contributes the limiting Poisson behavior of the sum, delineates the effect of extreme values, and leads to necessary and sufficient conditions all involving . It turns out that the limiting Poisson distributions arise in two qualitatively different ways depending upon whether >1 or <1. A concrete construction, illustrating all the results, also shows that in the boundary case when =1 both possibilities may occur. 相似文献
77.
We study perturbations of the quantized version
0 of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of
0 are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf 相似文献
78.
The osmotic pressures of –polyelectrolyte solutions without added salt was measured in the concentration ranges 0.001–0.02
and 0.2–1.9 mol kg-1. Our results show that the osmotic coefficients φp were strongly dependent on the chemical structures of polyelectrolyte through the polyion radius and the interaction between
the ionic moiety and counterions. The osmotic pressures in polyelectrolyte solutions without added salt, calculated on the
basis of the counterion contribution, are in agreement with the experimental results. We conclude that the counterion contribution
is dominant in the osmotic pressures and thus, the polymer contribution is negligible in the examined concentration range
0.2–1.9 mol kg-1. The P–B approach gave a fair prediction of the absolute values of the osmotic pressures with λ=4.5, where λ is the charge
density parameter, except for NaPA. In other words, the concentration dependence of the φp values can be explained in terms of the counterion contribution.
Received: 11 June 1997 Accepted: 19 August 1997 相似文献
79.
《Optimization》2012,61(5):743-754
In this paper the problem of estimation of an optimal replacement interval for a system which is minimally repaired at failures is studied. The problem is investigated both under a parametric and a nonparametric form of the failure intensity of the system. It is assumed that observational data from n systems are available. Some asymptotic results are shown. A graphical procedure for determining/estimating an optimal replacement interval is presented. The procedure is particularly valuable for sensitivity analyses, for example with respect to the costs involved. 相似文献
80.
Defect turbulence described by the one-dimensional complex Ginzburg–Landau equation is investigated and analyzed via a birth–death process of the local structures composed of defects, holes, and modulated amplitude waves (MAWs). All the number statistics of each local structure, in its stationary state, are subjected to Poisson statistics. In addition, the probability density functions of interarrival times of defects, lifetimes of holes, and MAWs show the existence of long-memory and some characteristic time scales caused by zigzag motions of oscillating traveling holes. The corresponding stochastic process for these observations is fully described by a non-Markovian master equation. 相似文献