共查询到20条相似文献,搜索用时 62 毫秒
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Dirichlet分布是一种重要的多维连续概率分布族,广泛应用于贝叶斯统计,是成分数据和比例数据建模中变量分布类型的自然选择.本文对其所具有的优良统计性质进行了汇总证明. 相似文献
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针对定解区域是无界区域的Dirichlet外问题,提出了一种新的有效的概率数值方法,它是从解的随机表达式出发,将无界区域上的问题转化成区域边界上的问题.此时,只要在边界上进行剖分,将问题离散化,然后在无界区域外的有界区域内构作一个辅助球,并且利用布朗运动、漂移布朗运动从球外一点出发,首中球面的位置和时间的分布等,就可以获得Dirichlet外问题的数值解. 相似文献
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该文研究了一般随机Dirichlet级数的所表示整函数增长性和值分布,得出了重要结论:在适当条件下,任何水平带形上或水平线上增长级与全面上相同,对于ρ随机Dirichlet级数(0<ρ<∞)a.s.在任何宽为〖SX(〗π[]ρ〖SX)〗的水平带形内,至少有一条ρ级没有有穷例外值的Borel线。 相似文献
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本文研究了Dirichlet分布总体的参数和其他感光趣的量的贝叶斯估计。在参数的有实际意义的函数上设置均匀的先验分布,对适当变换后的参数用Metropolis算法得到马尔可夫链蒙特卡罗后验样本,由此即得参数和其他感兴趣的量的贝叶斯估计。 相似文献
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LiWei Hai-liangYang 《应用数学学报(英文版)》2004,20(3):495-506
In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results. 相似文献
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N. Cressie and T. R. C. Read (1984, J. Roy. Statist. Soc. B46, 440–464) introduced a class of multinomial goodness-of-fit statistics Ra based on power divergence. All Ra have the same chi-square limiting distribution under null hypothesis and have the same noncentral chi-square limiting distribution under local alternatives. In this paper, we investigate asymptotic approximations for the distributions of Ra under local alternatives. We obtain an expression of approximation for the distribution of Ra under local alternatives. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, we propose a new approximation of the power of Ra. We call the approximation AE approximation. By numerical investigation of the accuracy of the AE approximation, we present a range of sample size n that the omission of the discontinuous term exercises only slight influence on power approximation of Ra. We find that the AE approximation is effective for a much wider range of the value of a than the other power approximations, except for an approximation method which requires high computer performance. 相似文献
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汪飞星 《数学物理学报(A辑)》1997,17(3):267-273
该文引进和讨论了退化矩阵Liouville分布,由此导出退化矩阵Beta分布、退化矩阵Dirichlet分布.推广了文献[1]关于退化Wishart分布和秩为1的退化矩阵Beta分布的结果。 相似文献
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Within the framework of Bayesian inference, when observations are exchangeable and take values in a finite space X, a prior P is approximated (in the Prokhorov metric) with any precision by explicitly constructed mixtures of Dirichlet distributions. Likewise, the posteriors are approximated with some precision by the posteriors of these mixtures of Dirichlet distributions. Approximations in the uniform metric for distribution functions are also given. These results are applied to obtain a method for eliciting prior beliefs and to approximate both the predictive distribution (in the variational metric) and the posterior distribution function of d
(in the Lévy metric), when
is a random probability having distribution P. 相似文献
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Asymptotic expansions for large deviation probabilities are used to approximate the cumulative distribution functions of noncentral generalized chi-square distributions, preferably in the far tails. The basic idea of how to deal with the tail probabilities consists in first rewriting these probabilities as large parameter values of the Laplace transform of a suitably defined function fk; second making a series expansion of this function, and third applying a certain modification of Watson's lemma. The function fk is deduced by applying a geometric representation formula for spherical measures to the multivariate domain of large deviations under consideration. At the so-called dominating point, the largest main curvature of the boundary of this domain tends to one as the large deviation parameter approaches infinity. Therefore, the dominating point degenerates asymptotically. For this reason the recent multivariate asymptotic expansion for large deviations in Breitung and Richter (1996, J. Multivariate Anal.58, 1–20) does not apply. Assuming a suitably parametrized expansion for the inverse g−1 of the negative logarithm of the density-generating function, we derive a series expansion for the function fk. Note that low-order coefficients from the expansion of g−1 influence practically all coefficients in the expansion of the tail probabilities. As an application, classification probabilities when using the quadratic discriminant function are discussed. 相似文献
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In this paper, a joint limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved. The explicit form of the limit measure is given. 相似文献
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Abstract Let X1,X2,...be a sequence of dependent and heavy-tailed random variables with distributions F1,F2,…. on (-∞,∞),and let т be a nonnegative integer-valued random variable independent of the seq... 相似文献
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This is the second in a series of three papers; the other two are “Summation Formulas, from Poisson and Voronoi to the Present” [Progr. Math. 220 (2004) 419-440] and “Automorphic Distributions, L-functions, and Voronoi Summation for GL(3)” (preprint). The first paper is primarily expository, while the third proves a Voronoi-style summation formula for the coefficients of a cusp form on . The present paper contains the distributional machinery used in the third paper for rigorously deriving the summation formula, and also for the proof of the GL(3)×GL(1) converse theorem given in the third paper. The primary concept studied is a notion of the order of vanishing of a distribution along a closed submanifold. Applications are given to the analytic continuation of Riemann's zeta function, degree 1 and degree 2 L-functions, the converse theorem for GL(2), and a characterization of the classical Mellin transform/inversion relations on functions with specified singularities. 相似文献
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A. Laurinčikas 《Lithuanian Mathematical Journal》1999,39(3):262-272
Using some conjectures on the mean-value of generalized numbers, limit theorems in the sense of the weak convergence of probability
measures for the Dirichlet series related to the Euler function are proved. Also, the limit measure is studied.
Partially supported by the Lithuanian State Science and Studies Foundation.
Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania: Šiauliai University, P. Višinskio 25, 5400 Šiauliai, Lithuania.
Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 331–342, July–September, 1999.
Translated by A. Laurinčikas 相似文献
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MM Algorithms for Some Discrete Multivariate Distributions 总被引:1,自引:0,他引:1
《Journal of computational and graphical statistics》2013,22(3):645-665
The MM (minorization–maximization) principle is a versatile tool for constructing optimization algorithms. Every EM algorithm is an MM algorithm but not vice versa. This article derives MM algorithms for maximum likelihood estimation with discrete multivariate distributions such as the Dirichlet-multinomial and Connor–Mosimann distributions, the Neerchal–Morel distribution, the negative-multinomial distribution, certain distributions on partitions, and zero-truncated and zero-inflated distributions. These MM algorithms increase the likelihood at each iteration and reliably converge to the maximum from well-chosen initial values. Because they involve no matrix inversion, the algorithms are especially pertinent to high-dimensional problems. To illustrate the performance of the MM algorithms, we compare them to Newton’s method on data used to classify handwritten digits. 相似文献