共查询到20条相似文献,搜索用时 46 毫秒
1.
B. Grigelionis 《Acta Appl Math》1999,58(1-3):125-134
A triangular array of independent infinitesimal integer-valued random variables is considered. Asymptotic expansions for the probability distributions of sums of these variables are investigated in the case of the limiting compound Poisson laws. 相似文献
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G. Bareikis 《Lithuanian Mathematical Journal》2004,44(4):342-353
We consider the asymptotic behavior of the distributions of arithmetic functions in polynomial semigroups.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 429–442, October–December, 2004. 相似文献
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We consider the limit distribution of values of a sum of additive arithmetic functions with shifted argument. The case of
the Poisson limit distribution is studied. The functions considered take at most two values on the set of primes, 0 and 1,
and satisfy some additional conditions. Some examples are given.
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John Panaretos Evdokia Xekalaki 《Annals of the Institute of Statistical Mathematics》1986,38(1):223-231
Summary The binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications.
The present paper examines some generalizations of these distributions with many practical applications. Properties of these
generalizations are studied and models giving rise to them are developed. Finally, their relationship to generalized Poisson
distributions is examined and limiting cases are given. 相似文献
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Yasuki Kikuchi Takashi Yanagawa 《Annals of the Institute of Statistical Mathematics》1988,40(2):367-379
An exact conditional test is developed for testing a trend in Poisson means when the historical control information is incorporated into the concurrent control data. An asymptotic conditional test is also developed as an alternative to the Tarone test. Asymptotic gains by the incorporation of the historical information is evaluated. 相似文献
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Olivier Collier Arnak S. Dalalyan 《Statistical Inference for Stochastic Processes》2018,21(2):331-344
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity vectors, under the assumption that most of them coincide with a given “background” signal. The number s of p-dimensional signals different from the background signal plays the role of sparsity and the goal is to leverage this sparsity assumption in order to improve the quality of estimation as compared to the naive estimator that computes the sum of the observed signals. We first introduce the group hard thresholding estimator and analyze its mean squared error measured by the squared Euclidean norm. We establish a nonasymptotic upper bound showing that the risk is at most of the order of \(\sigma ^2(sp+s^2\sqrt{p}\log ^{3/2}(np))\). We then establish lower bounds on the minimax risk over a properly defined class of collections of s-sparse signals. These lower bounds match with the upper bound, up to logarithmic terms, when the dimension p is fixed or of larger order than \(s^2\). In the case where the dimension p increases but remains of smaller order than \(s^2\), our results show a gap between the lower and the upper bounds, which can be up to order \(\sqrt{p}\). 相似文献
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Roelof Helmers I. Wayan Mangku 《Annals of the Institute of Statistical Mathematics》2009,61(3):599-628
We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson
process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in
a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The
asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed. A simulation study shows
that the first order asymptotic approximations to the bias and variance of the estimator are not accurate enough. Second order
terms for bias and variance were derived in order to be able to predict the numerical results in the simulation. Bias reduction
of our estimator is also proposed. 相似文献
10.
复合泊松过程的可加性 总被引:1,自引:0,他引:1
对复合泊松分布可加性的研究在许多的文献中都可以看到,本文首先应用特征函数的方法证明了复合泊松分布的可加性.以此为基础,结合对随机过程相关性质的讨论,证明了复合泊松过程也具有与复合泊松分布可加性相似的,某种意义上的可加性性质. 相似文献
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计数数据往往存在过离散(over-dispersed)即方差大于均值特征,若利用传统的泊松回归模型拟合数据往往会导致其参数的标准误差被低估,显著性水平被高估的错误结论。负二项回归模型、广义泊松回归模型通常被用来处理过离散特征数据。本文以两类广义泊松回归模型GP-1和GP-2模型为基础,将其推广为更为一般的GP-P形式,其中P为参数。此时,P=1或P=2,GP-P模型就退化为GP-1和GP-2模型。文中最后利用此类推广的GP-P模型处理了一组医疗保险数据,并与泊松回归模型、负二项回归模型拟合结果进行了比较。结果表明,推广后的GP-P模型的拟合效果更优。 相似文献
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A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors. 相似文献
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Roelof Helmers Qiying Wang Ričardas Zitikis 《Statistical Inference for Stochastic Processes》2009,12(1):21-36
A classical approach to constructing simultaneous confidence intervals (i.e., confidence bands or regions) for a function
is via establishing a limiting process of the appropriately normalized difference between the function and its empirical estimator.
In the present paper we depart from this approach and construct confidence bands for the intensity function of a cyclic Poisson
process via extreme value type asymptotic results for the appropriately normalized supremum of the difference between the
intensity function and its empirical estimator.
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14.
Denuit Michel Lefèvre Claude Shaked Moshe 《Methodology and Computing in Applied Probability》2000,2(3):231-254
This paper is devoted to the study of the compound Poisson mixture model in an actuarial framework. Using the s-convex stochastic orderings and stochastic s-convexity, several problems involving an unknown mixing parameter with given moments are examined; namely, the specification of the number of support points in a finite mixture model, and the derivation of extremal mixture distributions. The theory is enhanced with the derivation of theoretical and numerical bounds on several quantities of actuarial interest. 相似文献
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F. Móricz 《Acta Mathematica Hungarica》2002,98(3):259-262
A theorem of Ferenc Lukács determines the jumps of a periodic, Lebesgue integrable function f at each point of discontinuity of first kind in terms of the partial sums of the conjugate series to the Fourier series of
f. The aim of this note is to prove an analogous theorem in terms of the Abel-Poisson means.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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两参数广义Poisson过程 总被引:6,自引:0,他引:6
定义了两参数广义Poisson过程,得到了它的基本性质、局部鞅性和各种两参数Markov性,研究了它的跳线和样本函数,对跳线和样本函数作了形象、明确和深刻的刻划,可以说是一目了然的。 相似文献
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Fractional Poisson process 总被引:1,自引:0,他引:1
A fractional non-Markov Poisson stochastic process has been developed based on fractional generalization of the Kolmogorov–Feller equation. We have found the probability of n arrivals by time t for fractional stream of events. The fractional Poisson process captures long-memory effect which results in non-exponential waiting time distribution empirically observed in complex systems. In comparison with the standard Poisson process the developed model includes additional parameter μ. At μ=1 the fractional Poisson becomes the standard Poisson and we reproduce the well known results related to the standard Poisson process.As an application of developed fractional stochastic model we have introduced and elaborated fractional compound Poisson process. 相似文献
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Wen Su Yaodi Yong Zhimin Zhang 《Journal of Mathematical Analysis and Applications》2019,469(2):705-729
In this paper, we study the statistical estimation of the Gerber–Shiu function in the compound Poisson risk model perturbed by diffusion. This problem has been solved in [32] by the Fourier–Sinc series expansion method. Different from [32], we use the Laguerre series to expand the Gerber–Shiu function and propose a relevant estimator. The estimator is easily computed and has fast convergence rate. Various simulation studies are presented to confirm that the estimator performs well when the sample size is finite. 相似文献
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