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We present an integral test to determine the limiting behavior of weighted sums of independent, symmetric random variables with stable distributions, and deduce Chover-type laws of the iterated logarithm for them.  相似文献   

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We obtain the limiting distribution of the time averages of processes with a semi-Markov interference without assuming the finiteness of the moments of the interference time.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 281–284, February, 1990.  相似文献   

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We estimate the integral closeness of the Poisson, the Polya, and the negative Polya distributions to the normal. Some previous results on normal approximation to binomial and hypergeometric distributions are generalized.Translated from Statisticheskie Metody, pp. 104–113, 1980.  相似文献   

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In this paper, the process {X(t); t>0}, representing the position of a uniformly accelerated particle (with Poisson-paced) changes of its acceleration, is studied. It is shown that the distribution ofX(t) (suitably normalized), conditionally on the numbern of changes of acceleration, tends in distribution to a normal variate asn goes to infinity. The asymptotic normality of the unconditional distribution ofX(t) for large values oft is also shown. The study of these limiting distributions is motivated by the difficulty of evaluating exactly the conditional and unconditional probability laws ofX(t). In fact, the results obtained in this paper permit us to give useful approximations of the probability distributions of the position of the particle. Dipartmento di Statistica, Probabilità Statistiche Applicate University of Rome “La Sapienza,” Italy. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 3, pp. 295–308, July–September, 1997.  相似文献   

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For fixed p (0 ≤ p ≤ 1), let {L0, R0} = {0, 1} and X1 be a uniform random variable over {L0, R0}. With probability p let {L1, R1} = {L0, X1} or = {X1, R0} according as X112(L0 + R0) or < 12(L0 + R0); with probability 1 ? p let {L1, R1} = {X1, R0} or = {L0, X1} according as X112(L0 + R0) or < 12(L0 + R0), and let X2 be a uniform random variable over {L1, R1}. For n ≥ 2, with probability p let {Ln, Rn} = {Ln ? 1, Xn} or = {Xn, Rn ? 1} according as Xn12(Ln ? 1 + Rn ? 1) or < 12(Ln ? 1 + Rn ? 1), with probability 1 ? p let {Ln, Rn} = {Xn, Rn ? 1} or = {Ln ? 1, Xn} according as Xn12(Ln ? 1 + Rn ? 1) or < 12(Ln ? 1 + Rn ? 1), and let Xn + 1 be a uniform random variable over {Ln, Rn}. By this iterated procedure, a random sequence {Xn}n ≥ 1 is constructed, and it is easy to see that Xn converges to a random variable Yp (say) almost surely as n → ∞. Then what is the distribution of Yp? It is shown that the Beta, (2, 2) distribution is the distribution of Y1; that is, the probability density function of Y1 is g(y) = 6y(1 ? y) I0,1(y). It is also shown that the distribution of Y0 is not a known distribution but has some interesting properties (convexity and differentiability).  相似文献   

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Summary X 1,...,X n are independent random variables, identically distributed over the unit interval, with common probability density function 1 + r(x)/n for all sufficiently large n, where is a positive constant, and |r(x)| <D. V 1, ..., V n+1 are the sample spacings generated by X 1,..., X n . It is shown that in many cases, the asymptotic joint distribution of homogeneous functions of V 1,..., V n+1 can be found directly from the asymptotic joint distribution of homogeneous functions of independent exponential random variables.Research supported by NSF Grant GP 3783.  相似文献   

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U — [0, 1] Y — . X=[1–U 1/v /Y], U Y.  相似文献   

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We use the method of moments to establish the limiting spectral distribution (LSD) of appropriately scaled large dimensional random symmetric circulant, reverse circulant, Toeplitz and Hankel matrices which have suitable band structures. The input sequence used to construct these matrices is assumed to be either i.i.d. with mean zero and variance one or independent and appropriate finite fourth moment. The class of LSD includes the normal and the symmetrized square root of chi-square with two degrees of freedom. In several other cases, explicit forms of the limit do not seem to be obtainable but the limits can be shown to be symmetric and their second and the fourth moments can be calculated with some effort. Simulations suggest some further properties of the limits.  相似文献   

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Let \s{Xn, n ? 0\s} and \s{Yn, n ? 0\s} be two stochastic processes such that Yn depends on Xn in a stationary manner, i.e. P(Yn ? A\vbXn) does not depend on n. Sufficient conditions are derived for Yn to have a limiting distribution. If Xn is a Markov chain with stationary transition probabilities and Yn = f(Xn,..., Xn+k) then Yn depends on Xn is a stationary way. Two situations are considered: (i) \s{Xn, n ? 0\s} has a limiting distribution (ii) \s{Xn, n ? 0\s} does not have a limiting distribution and exits every finite set with probability 1. Several examples are considered including that of a non-homogeneous Poisson process with periodic rate function where we obtain the limiting distribution of the interevent times.  相似文献   

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Phase-type (PH) probability distributions provide a versatile class of distributions, and are shown to fit naturally into a Markovian compartmental system, where “individuals” or “particles” move between a series of compartments, so that phase-type compartmental residence-time distributions can be incorporated simply by increasing the size of the system. Examples of PH distributions covering a variety of behaviours are given, and an application involving data analysis is included.  相似文献   

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Translated from Problemy Ustoichivpsti Stokhasticheskikh Modelei, Trudy Seminara, pp. 83–89, 1987.  相似文献   

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Annals of the Institute of Statistical Mathematics - Consider a p-variate normal random vector. We are interested in the limiting distributions of likelihood ratio test (LRT) statistics for testing...  相似文献   

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Following the approach suggested by I. Kaj and M. Taqqu, we consider a stochastic model of teletraffic based on Poisson random measure. We show that under appropriate assumptions, the finite-dimensional distributions for the scaled workload process converge to those of a stable Lévy process. Bibliography: 10 titles.  相似文献   

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