Poisson过程中的几何分布

讨论变环境系统可靠性维修过程中,t0,t1,…,tN内复杂系统出现故障的变参数Poisson过程.利用强马氏性定理证明不同类故障间距次数Xnk的独立性,给出不同子系统或元器件出现不同故障类型的概率分布:变参数几何分布Xnk～Geometric(pk),同时验证了几何分布的变动统计特性.     

A Geometric Characterization of a Class of Poisson Type Distributions

Tempered distributions on \(\mathbb {R}^{n}\) which have Dirac comb structure are characterized in terms of sparseness properties of its support and spectrum.     

Geometric ergodicity of the Gibbs sampler for the Poisson change-point model

Poisson change-point models have been widely used for modelling inhomogeneous time-series of count data. There are a number of methods available for estimating the parameters in these models using iterative techniques such as MCMC. Many of these techniques share the common problem that there does not seem to be a definitive way of knowing the number of iterations required to obtain sufficient convergence. In this paper, we show that the Gibbs sampler of the Poisson change-point model is geometrically ergodic. Establishing geometric ergodicity is crucial from a practical point of view as it implies the existence of a Markov chain central limit theorem, which can be used to obtain standard error estimates. We prove that the transition kernel is a trace-class operator, which implies geometric ergodicity of the sampler. We then provide a useful application of the sampler to a model for the quarterly driver fatality counts for the state of Victoria, Australia.     

On some properties of Poisson processes

The Poisson process, i.e., the simple stream, is defined by Khintchine as a stationary, orderly and finite stream without after-effects. A necessary and sufficient condition for a stream to be a simple stream is that the interarrival times are independent random variables with identical exponential distributions. This paper gives a simple and rigorous proof of the necessary and sufficient condition, and discusses the other necessary and sufficient conditions for a renewal process to be a Poisson process.Institute of Applied Mathematics, Academia Sinica     

On distance-3 matchings and induced matchings

For a finite undirected graph G=(V,E) and positive integer k≥1, an edge set M⊆E is a distance-k matching if the pairwise distance of edges in M is at least k in G. For k=1, this gives the usual notion of matching in graphs, and for general k≥1, distance-k matchings were called k-separated matchings by Stockmeyer and Vazirani. The special case k=2 has been studied under the names induced matching (i.e., a matching which forms an induced subgraph in G) by Cameron and strong matching by Golumbic and Laskar in various papers.Finding a maximum induced matching is NP-complete even on very restricted bipartite graphs and on claw-free graphs but it can be done efficiently on various classes of graphs such as chordal graphs, based on the fact that an induced matching in G corresponds to an independent vertex set in the square L(G)² of the line graph L(G) of G which, by a result of Cameron, is chordal for any chordal graph G.We show that, unlike for k=2, for a chordal graph G, L(G)³ is not necessarily chordal, and finding a maximum distance-3 matching, and more generally, finding a maximum distance-(2k+1) matching for k≥1, remains NP-complete on chordal graphs. For strongly chordal graphs and interval graphs, however, the maximum distance-k matching problem can be solved in polynomial time for every k≥1. Moreover, we obtain various new results for maximum induced matchings on subclasses of claw-free graphs.     

Algebraic properties of compatible Poisson brackets

We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A(x) and B(x). From the algebraic viewpoint this amounts to studying the properties of a pair of skew-symmetric bilinear forms A and B defined on a finite-dimensional vector space. We describe the Lie group G _P of linear automorphisms of the pencil P = {A + λB}. In particular, we obtain an explicit formula for the dimension of G _P and discuss some other algebraic properties such as solvability and Levi-Malcev decomposition.     

Geometric properties of the tetrablock

In this short note, we show that the tetrablock is a ${\mathbb{C}}$ -convex domain. In the proof of this fact, a new class of ( ${\mathbb{C}}$ -convex) domains is studied. The domains are natural candidates to study on them the behavior of holomorphically invariant functions.     

Poisson and compound Poisson distributions of order k and some of their properties

One investigates the Poisson distribution of orderk. One finds its generating function and with its aid one establishes that the sum of independent random variables, distributed according to the Poisson law of orderk, is distributed in the same manner. In addition, one considers a generalized compound Poisson distribution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 175–180, 1983.     

Geometric properties of the double-point divisor

The locus of double points obtained by projecting a variety to a hypersurface in moves in a linear system which is shown to be ample if and only if is not an isomorphic projection of a Roth variety. Such Roth varieties are shown to exist, and some of their geometric properties are determined.

     

Geometric properties of the heat content

In this paper we study the short time behavior of heat semigroup in connection with the geometry of sets with finite perimeter; we assume C ^1,1 regularity and we relate the heat semigroup with curvatures of the initial datum. We also study the behavior when singularities occur; this is the case when the mean curvature is no more a function, but has to be considered as a Radon measure. This work is the natural continuation of Miranda et al. (Ann Fac Sci Toulouse Math (6) 16(1):125–145, 2007) and is in the spirit of van den Berg and Le Gall (Math Z 215(3):437–464, 1994).     

Geometric properties of basic hypergeometric functions

In this article, we consider basic hypergeometric functions introduced by Heine. We study the mapping properties of certain ratios of basic hypergeometric functions having shifted parameters and show that they map the domains of analyticity onto domains convex in the direction of the imaginary axis. In order to investigate these mapping properties, some useful identities are obtained in terms of basic hypergeometric functions. In addition, we find conditions under which the basic hypergeometric functions are in a q-close-to-convex family.     

Geometric properties of F-normed Orlicz spaces

Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern...     

Geometric properties of the Cassinian metric

In this paper we prove a sharp distortion property of the Cassinian metric under Möbius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in proper subdomains of . Inclusion properties of the Cassinian metric balls with other hyperbolic‐type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.     

On optimal matchings

Givenn random red points on the unit square, the transportation cost between them is tipically √n logn.     

关于二项分布、Poisson分布和几何分布的高阶矩的递推公式

给出了二项分布、Poisson分布和几何分布高阶矩的递推公式,避免了其它计算方法上的不便与误差.     

Alternating cycle-free matchings

The investigation of alternating cycle-free matchings is motivated by the Jump-number problem for partially ordered sets and the problem of counting maximum cardinality matchings in hexagonal systems.We show that the problem of deciding whether a given chordal bipartite graph has an alternating cycle-free matching of a given cardinality is NP-complete. A weaker result, for bipartite graphs only, has been known for some time. Also, the alternating cycle-free matching problem remains NP-complete for strongly chordal split graphs of diameter 2.In contrast, we give algorithms to solve the alternating cycle-free matching problem in polynomial time for bipartite distance hereditary graphs (time O(m ²) on graphs with m edges) and distance hereditary graphs (time O(m ⁵)).