Poisson Models and Parametric Inference

2013 ◽  
pp. 23-45
Author(s):  
Jianguo Sun ◽  
Xingqiu Zhao
Keyword(s):  
Parametric Inference ◽  
Poisson Models

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals A Variance Gamma model for Rugby Union matches

2020 ◽  
Vol 17 (1) ◽  
pp. 67-75
Author(s):  
John Fry ◽  
Oliver Smart ◽  
Jean-Philippe Serbera ◽  
Bernhard Klar
Keyword(s):  
Three Dimensional ◽  
Rugby Union ◽  
Three Dimensional Model ◽  
Gamma Model ◽  
Variance Gamma ◽  
Poisson Models ◽  
History Of ◽  
Bonus Points ◽  
Variance Gamma Model ◽  
Special Case

Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

scholarly journals Agricultural drought periods analysis by using nonhomogeneous poisson models and regionalization of appropriate model parameters

2021 ◽  
Vol 73 (1) ◽  
pp. 1-15
Author(s):  
Asad Ellahi ◽  
Ijaz Hussain ◽  
Muhammad Zaffar Hashmi ◽  
Mohammed Mohammed Ahmed Almazah ◽  
Fuad S. Al-Duais
Keyword(s):  
Agricultural Drought ◽  
Model Parameters ◽  
Poisson Models

scholarly journals Communicative efficiency and differential case marking: a reverse-engineering approach

2021 ◽  
Vol 7 (s3) ◽  
Author(s):  
Natalia Levshina
Keyword(s):  
Reverse Engineering ◽  
Conditional Probabilities ◽  
Case Marking ◽  
Poisson Models ◽  
Linguistic Patterns ◽  
Cue Reliability ◽  
Communicative Efficiency ◽  
Cue Availability ◽  
Probabilistic Measures ◽  
Better Than

Abstract The use of differential case marking of A and P has been explained in terms of efficiency (economy) and markedness. The present study tests predictions based on these accounts, using conditional probabilities of a particular feature given the syntactic role (cue availability), and conditional probabilities of a particular syntactic role given the feature in question (cue reliability). Cue availability serves as a measure of markedness, whereas cue reliability is central for the efficiency account. Similar to reverse engineering, we determine which of the probabilistic measures could have been responsible for the recurrent cross-linguistic patterns described in the literature. The probabilities are estimated from spontaneous informal dialogues in English and Russian (Indo-European), Lao (Tai-Kadai), N||ng (Tuu) and Ruuli (Bantu). The analyses, which involve a series of mixed-effects Poisson models, clearly demonstrate that cue reliability matches the observed cross-linguistic patterns better than cue availability. Thus, the results support the efficiency account of differential marking.

scholarly journals An Application Comparison of Two Poisson Models on Zero Count Data

2021 ◽  
Vol 1818 (1) ◽  
pp. 012165
Author(s):  
L. H. Hashim ◽  
K. H. Hashim ◽  
Mushtak A. K. Shiker
Keyword(s):  
Count Data ◽  
Poisson Models

scholarly journals Application of Transformations in Parametric Inference

2008 ◽  
Vol 16 (1) ◽  
Author(s):  
Naomi Brownstein ◽  
Marianna Pensky
Keyword(s):  
Parametric Inference

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

2011 ◽  
Vol 22 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Jorge A. Achcar ◽  
Eliane R. Rodrigues ◽  
Guadalupe Tzintzun
Keyword(s):  
Mexico City ◽  
Change Points ◽  
Poisson Models

Communicating across educational boundaries: accommodation patterns in adolescents’ online interactions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lisa Hilte ◽  
Walter Daelemans ◽  
Reinhild Vandekerckhove
Keyword(s):  
Online Communication ◽  
Educational Communication ◽  
Educational Background ◽  
Online Behavior ◽  
School Students ◽  
Demographic Profiles ◽  
Poisson Models ◽  
Variation Patterns ◽  
Linguistic Accommodation ◽  
Salient Features

Abstract This paper studies linguistic accommodation patterns in a large corpus of private online conversations produced by Flemish secondary school students. We use Poisson models to examine whether the teenagers adjust their writing style depending on their interlocutor’s educational profile, while also taking into account the extent to which these adaptation patterns are influenced by the authors’ own educational background or by other aspects of their socio-demographic profiles. The corpus does reveal accommodation patterns, but the adjustments do not always mirror variation patterns related to educational profiles. While salient features like expressive markers seem to lead to pattern-matching, less salient features appear less prone to ‘adequate’ adjustment. Lack of familiarity with the online behavior of students from other educational tracks is a factor too, since online communication clearly proceeds primarily within ‘same-education’ networks. The focus on cross-educational communication is quite unique in this respect and highly relevant from a sociological perspective.

Sign in / Sign up

Export Citation Format

Share Document