scholarly journals Modeling User Return Time Using Inhomogeneous Poisson Process

2019 ◽  
pp. 37-44
Author(s):  
Mohammad Akbari ◽  
Alberto Cetoli ◽  
Stefano Bragaglia ◽  
Andrew D. O’Harney ◽  
Marc Sloan ◽  
...  
Keyword(s):  
Poisson Process ◽  
Return Time ◽  
Inhomogeneous Poisson Process

Misspecified change-point estimation problem for a Poisson process

2001 ◽  
Vol 38 (A) ◽  
pp. 122-130 ◽  
Author(s):  
Ali S. Dabye ◽  
Yury A. Kutoyants
Keyword(s):  
Maximum Likelihood ◽  
Poisson Process ◽  
Change Point ◽  
Maximum Likelihood Estimate ◽  
Intensity Function ◽  
Point Estimation ◽  
Lower Function ◽  
Inhomogeneous Poisson Process ◽  
Change Point Estimation ◽  
Unknown Point

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ∗. What is known are continuous bounding functions g and h such that g∗(t) ≤ g(t) ≤ h(t) ≤ h∗(t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h∗.

Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes

1994 ◽  
Vol 26 (1) ◽  
pp. 122-154 ◽  
Author(s):  
Stephen L. Rathbun ◽  
Noel Cressie
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Asymptotic Properties ◽  
Point Pattern ◽  
Spatial Point Pattern ◽  
Asymptotic Results ◽  
Borel Set ◽  
Inhomogeneous Poisson Process ◽  
Asymptotically Normal ◽  
Asymptotically Efficient

Consider a spatial point pattern realized from an inhomogeneous Poisson process on a bounded Borel set , with intensity function λ (s; θ), where . In this article, we show that the maximum likelihood estimator and the Bayes estimator are consistent, asymptotically normal, and asymptotically efficient as the sample region . These results extend asymptotic results of Kutoyants (1984), proved for an inhomogeneous Poisson process on [0, T] , where T →∞. They also formalize (and extend to the multiparameter case) results announced by Krickeberg (1982), for the spatial domain . Furthermore, a Cramér–Rao lower bound is found for any estimator of θ. The asymptotic properties of and are considered for modulated (Cox (1972)), and linear Poisson processes.

Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes

1994 ◽  
Vol 26 (01) ◽  
pp. 122-154 ◽  
Author(s):  
Stephen L. Rathbun ◽  
Noel Cressie
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Asymptotic Properties ◽  
Point Pattern ◽  
Spatial Point Pattern ◽  
Asymptotic Results ◽  
Borel Set ◽  
Inhomogeneous Poisson Process ◽  
Asymptotically Normal ◽  
Asymptotically Efficient

Consider a spatial point pattern realized from an inhomogeneous Poisson process on a bounded Borel set , with intensity function λ (s; θ), where . In this article, we show that the maximum likelihood estimator and the Bayes estimator are consistent, asymptotically normal, and asymptotically efficient as the sample region . These results extend asymptotic results of Kutoyants (1984), proved for an inhomogeneous Poisson process on [0, T] , where T →∞. They also formalize (and extend to the multiparameter case) results announced by Krickeberg (1982), for the spatial domain . Furthermore, a Cramér–Rao lower bound is found for any estimator of θ. The asymptotic properties of and are considered for modulated (Cox (1972)), and linear Poisson processes.

scholarly journals Uncited papers are not useless

2021 ◽  
pp. 1-19
Author(s):  
Michael Golosovsky ◽  
Vincent Larivière
Keyword(s):  
Social Sciences ◽  
Poisson Process ◽  
Peer Review ◽  
Poisson Statistics ◽  
Inhomogeneous Poisson Process ◽  
Scientific Disciplines ◽  
And Mathematics

Abstract We study citation dynamics of the papers published in three scientific disciplines (Physics, Economics, and Mathematics) and four broad scientific categories (Medical, Natural, Social Sciences, and Arts & Humanities). We measure the uncitedness ratio, namely, the fraction of uncited papers in these datasets and its dependence on the time following publication. These measurements are compared with the model of citation dynamics which considers acquiring citations as an inhomogeneous Poisson process. The model captures the fraction of uncited papers in our collections fairly well, suggesting that uncitedness is an inevitable consequence of the Poisson statistics. Peer Review https://publons.com/publon/10.1162/qss_a_00142

Misspecified change-point estimation problem for a Poisson process

2001 ◽  
Vol 38 (A) ◽  
pp. 122-130
Author(s):  
Ali S. Dabye ◽  
Yury A. Kutoyants
Keyword(s):  
Maximum Likelihood ◽  
Poisson Process ◽  
Change Point ◽  
Maximum Likelihood Estimate ◽  
Intensity Function ◽  
Point Estimation ◽  
Lower Function ◽  
Inhomogeneous Poisson Process ◽  
Change Point Estimation ◽  
Unknown Point

Consider an inhomogeneous Poisson process X on [0, T] whose unknown intensity function ‘switches' from a lower function g∗ to an upper function h∗ at some unknown point θ ∗. What is known are continuous bounding functions g and h such that g∗ (t) ≤ g(t) ≤ h(t) ≤ h∗ (t) for 0 ≤ t ≤ T. It is shown that on the basis of n observations of the process X the maximum likelihood estimate of θ ∗ is consistent for n →∞, and also that converges in law and in pth moment to limits described in terms of the unknown functions g∗ and h ∗.

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