Notes on discrete compound Poisson model with applications to risk theory

Zhang, Huiming; Liu, Yunxiao; Li, Bo

doi:10.1016/j.insmatheco.2014.09.012

Cited by 48 publications

(45 citation statements)

References 26 publications

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“…2014), generalizing the Poisson distribution with another distribution :The generating function is defined accordingly:where and with are parameters . We introduce the notation …”

Section: Resultsmentioning

confidence: 99%

“…(38) from Example 1, is defined only in terms of a multinomial expansion (Zhang et al. 2014). In general, the distribution corresponding to the generating function of Eq.…”

Section: Appendixmentioning

confidence: 99%

“…2014), applicable for one dimensional distributions. The most important of these is the Lévy - Adelson - Panjer recursion for the , given byIn practice, the sum often converges after a constant number of terms (i.e.…”

Section: Appendixmentioning

confidence: 99%

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General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

2018

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Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME’s. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription–translation network and Bateman’s model from nuclear physics. For both examples, multimodality was previously not reported.Electronic supplementary materialThe online version of this article (10.1007/s00285-018-1205-2) contains supplementary material, which is available to authorized users.

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“…2014), generalizing the Poisson distribution with another distribution :The generating function is defined accordingly:where and with are parameters . We introduce the notation …”

Section: Resultsmentioning

confidence: 99%

“…(38) from Example 1, is defined only in terms of a multinomial expansion (Zhang et al. 2014). In general, the distribution corresponding to the generating function of Eq.…”

Section: Appendixmentioning

confidence: 99%

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General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

2018

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“…A more general example comes from the following corollary, see also Zhang et al (2014). Corollary 2.3.…”

Section: Characterizationsmentioning

confidence: 99%

A characterization of signed discrete infinitely divisible distributions

Zhang

Kerns³

2017

Studia Scientiarum Mathematicarum Hungarica

Self Cite

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In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller's characterization of discrete infinitely divisible distributions to signed discrete infinitely divisible distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the Lévy-Wiener theorem. This is a special case of an open problem which is proposed by Sato (2014), Chaumont and Yor (2012). An analogous result involving characteristic functions is shown for signed integer-valued infinitely divisible distributions. We show that many distributions are DPCP by the non-zero p.g.f. property, such as the mixed Poisson distribution and fractional Poisson process. DPCP has some bizarre properties, and one is that the parameter λ in the DPCP class cannot be arbitrarily small.

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“…Population of high-density building development zone (P HDU ), area of road infrastructure (S TU ), area of educational zones, (S EDU ) and area of commercial zones (S COM ); based on the ratio between average and variance of these variables [3,19] used in the following equations to accident estimation:…”

Section: Analysis Zones Data Setmentioning

confidence: 99%

Road Accident Estimation Model in Urban Areas

Raicu¹,

Costescu²,

Burciu³

et al. 2017

Transport Problems

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Summary. Urban areas are significantly different in terms of traffic risk. In a decisive manner, they are the result of urban development policies. The shape, size and configuration of an entire urban area, the facilities to satisfy people and the need for mobility of goods, as well as behavioural attitudes of the population, are essential for a traffic pattern and its associated risks. In this framework, the purpose of this paper is to identify the effects of urban area characteristics on road accidents. Using specific spatial analysis, a model of accident estimation in the urban areas of Bucharest is developed. The study aims to provide useful tools for urban decision makers for a-priori analysis of the consequences of urban outline changes on traffic risks. MODÈLE D'ESTIMATION DES ACCIDENTS DE LA ROUTE DANS LES ZONES URBAINESRésumé. Les zones urbaines sont très différentes en termes de risque associé à la circulation. En manière décisive, ils sont le résultat des stratégies du développement urbain. La forme, la dimension et la configuration de l'ensemble de la région urbaine, l'offre pour satisfaire les besoins de mobilité des personnes et des marchandises, ainsi que les attitudes comportementales de la population sont essentielles pour le modèle de la circulation et le risque routier. Dans ce contexte, l'objectif de cet article est d'identifier les effets des caractéristiques des zones urbaines sur les accidents de la route. L'étude vise à fournir des décideurs dans la planification urbaine des instruments nécessaires pour analyser apriori les conséquences des changements de la structure urbaine sur le risque routier.

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Notes on discrete compound Poisson model with applications to risk theory

Cited by 48 publications

References 26 publications

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

A characterization of signed discrete infinitely divisible distributions

Road Accident Estimation Model in Urban Areas

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