The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations witho...

We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical result in the case of deterministic transformations of Poisson measures. The approach relies on moment and covariance identities for Poisson stochastic integral...

We show that each triangular Poisson Lie group can be decomposed into Poisson submanifolds each of which is a quotient of a symplectic manifold. The Marsden–Weinstein–Meyer symplectic reduction technique is then used to give a complete description of the symplectic foliation of all triangular Poisson structures on Lie groups. The results are illustrated in detail for the generalized Jordanian P...

Poisson regression models for count variables have been utilized in many applications. However, in many problems overdispersion and zeroinflation occur. We study in this paper regression models based on the generalized Poisson distribution (Consul (1989)). These regression models which have been used for about 15 years do not belong to the class of generalized linear models considered by McCull...

Abstract Using numerous transaction data on the number of stock trades, we conduct a forecasting exercise with INGARCH models, governed by various conditional distributions; Poisson, linear and quadratic negative binomial, double Poisson generalized Poisson. The model parameters are estimated efficient Markov Chain Monte Carlo methods, while forecast evaluation is done calculating point density...

The Poisson regression model is a simple count data that combines models in which the response variable form of counts rather than fractional numbers generalized linear (GLMs) . Three (Poisson regression, quasi-Poisson and negative binomial regression) were compared r packages applied to sample COVID-19 this study. was shown be best most efficient other models.

We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non-commutative setting. Partially supported by the Italian Consiglio Nazionale ...

We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets are always constant. Some examples are given alongside the general theory.

Martin-Löf randomness was originally defined and studied in the context of the Cantor space 2ω . In [1] probability theoretic random closed sets (RACS) are used as the foundation for the study of Martin-Löf randomness in spaces of closed sets. Here we focus on the space of closed subsets of R and a particular family of measures on this space, the generalized Poisson processes. This gives a nove...

In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This Mittag-Leffler function distribution (MLFD) belongs to the generalized hypergeometric and generalized power series families and also arises as weighted Poisson...