scholarly journals Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

2006 ◽  
Vol 82 (9) ◽  
pp. 167-172
Author(s):  
Eisuke Imamura ◽  
Kiyosato Okamoto ◽  
Michiroh Tsukamoto ◽  
Atsushi Yamamori
Keyword(s):  
Generalized Poisson ◽  
Cauchy Transforms

scholarly journals Eigenvalues of generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

2009 ◽  
Vol 39 (2) ◽  
pp. 237-275 ◽  
Author(s):  
Eisuke Imamura ◽  
Kiyosato Okamoto ◽  
Michiroh Tsukamoto ◽  
Atsushi Yamamori
Keyword(s):  
Generalized Poisson ◽  
Cauchy Transforms

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

GENERALIZED POISSON INTEGRAL AND ITS APPLIED ASPECTS

2021 ◽  
Vol 2 ◽  
pp. 102-111
Author(s):  
Ulyana Grabova ◽  
◽  
Svetlana Salnikova ◽  
Keyword(s):  
Game Theory ◽  
Social Dynamics ◽  
Optimal Strategies ◽  
Integral Representations ◽  
Periodic Functions ◽  
Mathematical Methods ◽  
Linear Processes ◽  
Generalized Poisson ◽  
Long Time ◽  
Autonomous Differential Equations

Mathematical methods based on statistics have been used in sociology for a long time. The functioning of socio-economic and socio-politic systems is a complex process, which is caused by a number of various factors. Thus, the construction of models of socio-economic and socio-politic processes requires solving problems of both the decomposition of structures and processes, and their integration into a single system model, taking into account the changing conditions of the external environment. Mathematical modeling of such problems can be carried out by methods of network analysis or game theory, which allows finding optimal strategies for the behavior of competitive parties. Asymptotic formulations have a central role in game theory, since, due to the complex strategic nature, explicit solutions can be found only in very rare cases. A large number of models created to study complex social processes that occur in society are dynamical systems, or non-autonomous differential equations, or difference equations with a large number of parameters in any cases. In this situation, it is important to choose an appropriate tool for studying the behavior of such systems. In this paper, generalized Poisson delta operators are considered as approximating aggregates, since periodic processes, which are subdivided into harmonic and polyharmonic, provide the internal integrity of complex systems and their dynamic functioning. Questions of the asymptotic behavior of the exact upper bounds for approximations by generalized Poisson delta operators on classes of periodic functions that satisfy the Lipschitz condition are also studied. The received formulas provide a solution to the Kolmogorov-Nikol’ski problem for generalized Poisson delta operators and Lipschitz classes. The proof is based on the use of formulas that give integral representations of the deviations of linear methods generated by linear processes of summation of Fourier series on sets of periodic functions in the uniform metric obtained in the works of L.I. Bausov. The results can be an effective tool for modeling the processes of social dynamics.

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