scholarly journals Separable and semiparametric network-based counting processes applied to the international combat aircraft trades

2021 ◽  
pp. 1-21
Author(s):  
Cornelius Fritz ◽  
Paul W. Thurner ◽  
Göran Kauermann
Keyword(s):  
Poisson Process ◽  
Random Effects ◽  
Network Data ◽  
Counting Processes ◽  
Time Varying ◽  
Political Factors ◽  
Combat Aircraft ◽  
Intensity Functions ◽  
Multivariate Poisson Process

Abstract We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs the onset and repetition of yearly observed events with two separate intensity functions. We apply the model to a network obtained from the yearly dyadic number of international deliveries of combat aircraft trades between 1950 and 2017. Based on the trade gravity approach, we identify economic and political factors impeding or promoting the number of transfers. Extensive dynamics as well as country heterogeneities require the specification of semiparametric time-varying effects as well as random effects. Our findings reveal strong heterogeneous as well as time-varying effects of endogenous and exogenous covariates on the onset and repetition of aircraft trade events.

Positional Estimation Within a Latent Space Model for Networks

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Susan Shortreed ◽  
Mark S. Handcock ◽  
Peter Hoff
Keyword(s):  
Random Effects ◽  
Network Data ◽  
Random Effects Models ◽  
Space Model ◽  
Network Analyses ◽  
Recent Advances ◽  
Latent Space ◽  
Latent Space Model ◽  
Modeling Data

Recent advances in latent space and related random effects models hold much promise for representing network data. The inherent dependency between ties in a network makes modeling data of this type difficult. In this article we consider a recently developed latent space model that is particularly appropriate for the visualization of networks. We suggest a new estimator of the latent positions and perform two network analyses, comparing four alternative estimators. We demonstrate a method of checking the validity of the positional estimates. These estimators are implemented via a package in the freeware statistical language R. The package allows researchers to efficiently fit the latent space model to data and to visualize the results.

Operator-based intensity functions for the nonhomogeneous Poisson process

2016 ◽  
Vol 25 (2) ◽  
pp. 79-98 ◽  
Author(s):  
S. K. Bar-Lev ◽  
D. Bshouty ◽  
F. A. van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Nonhomogeneous Poisson Process ◽  
Intensity Functions

scholarly journals On the equivalence of various definitions of mixed poisson processes

2019 ◽  
Vol 69 (2) ◽  
pp. 453-468
Author(s):  
Demetrios P. Lyberopoulos ◽  
Nikolaos D. Macheras ◽  
Spyridon M. Tzaninis
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Random Variable ◽  
Poisson Processes ◽  
Counting Processes ◽  
Mixing Parameter ◽  
Mixed Poisson Process ◽  
Probability Spaces ◽  
The One

Abstract Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing probability distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of “canonical” probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions for the characterization of mixed Poisson processes in terms of disintegrations cannot be omitted.

scholarly journals A martingale characterization of Pólya-Lundberg processes

2006 ◽  
Vol 43 (03) ◽  
pp. 741-754 ◽  
Author(s):  
Birgit Niese
Keyword(s):  
Poisson Process ◽  
Exponential Family ◽  
Exponential Families ◽  
Counting Processes ◽  
Mixed Poisson Process ◽  
Martingale Characterization

We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

scholarly journals Counting processes with Bernštein intertimes and random jumps

2015 ◽  
Vol 52 (04) ◽  
pp. 1028-1044 ◽  
Author(s):  
Enzo Orsingher ◽  
Bruno Toaldo
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Negative Binomial ◽  
Counting Processes ◽  
Lévy Measure ◽  
Fractional Poisson Process ◽  
Independent Increments ◽  
Random Jumps ◽  
The Times ◽  
Passage Times

In this paper we consider point processes Nf (t), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernštein functions f with Lévy measure v. We obtain the general expression of the probability generating functions Gf of Nf , the equations governing the state probabilities pk f of Nf , and their corresponding explicit forms. We also give the distribution of the first-passage times Tk f of Nf , and the related governing equation. We study in detail the cases of the fractional Poisson process, the relativistic Poisson process, and the gamma-Poisson process whose state probabilities have the form of a negative binomial. The distribution of the times of jumps with height lj () under the condition N(t) = k for all these special processes is investigated in detail.

scholarly journals Study on reservoir time-varying design flood of inflow based on Poisson process with time-dependent parameters

2018 ◽  
Vol 379 ◽  
pp. 119-123
Author(s):  
Jiqing Li ◽  
Jing Huang ◽  
Jianchang Li
Keyword(s):  
Poisson Process ◽  
Flood Control ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Design Flood ◽  
Threshold Method ◽  
Peak Over Threshold ◽  
Peak Over Threshold Method ◽  
The Relationship

Abstract. The time-varying design flood can make full use of the measured data, which can provide the reservoir with the basis of both flood control and operation scheduling. This paper adopts peak over threshold method for flood sampling in unit periods and Poisson process with time-dependent parameters model for simulation of reservoirs time-varying design flood. Considering the relationship between the model parameters and hypothesis, this paper presents the over-threshold intensity, the fitting degree of Poisson distribution and the design flood parameters are the time-varying design flood unit period and threshold discriminant basis, deduced Longyangxia reservoir time-varying design flood process at 9 kinds of design frequencies. The time-varying design flood of inflow is closer to the reservoir actual inflow conditions, which can be used to adjust the operating water level in flood season and make plans for resource utilization of flood in the basin.

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