Background & Aim: Statistical modeling is one of the most suitable methods for analyzing the relationship between health and medical issues. In the situation of analysis of zero-inflated data, there are different methods. In this study, the models Poisson, Poisson gamma, and Poisson lognormal regression were compared.Methods & Materials: This cross-sectional study was conducted to determine the influential factors on decay-missing-filled (DMF) index by the three mentioned models using the data of 808 first-grade children of the primary school in Kerman, Iran. The command PROC NLMIXED in SAS software was applied for fitting the models on data. For comparing the models, we applied the Akaike’s criterion (AIC), mean square error (MSE) criterion and confidence interval (CI).Results: The AIC and CI showed that the Poisson lognormal model was better than the others due to a level of significance. The variables of the students’ place of living, mothers’ jobs, fathers’ jobs, the region, sex, optic problems, and behavioral problems had a significant effect on DMF index.Conclusion: Poisson lognormal was better than the other models in dental health data.

The paper develops the methods for computer simulation of the dynamics of absolutely rigid body systems with a tree structure. The equations of motion are presented in compact matrix form. The case of holonomic constraints is also considered. Since the independent parameters uniquely determine the positions and velocities of the bodies of the system in space, the generalized coordinates and variables with the dimension of impulses are chosen. A feature of the system of equations is that it is resolved with respect to the derivatives of the generalized momenta and does not contain constraint reactions. The derivation of the proposed form of the equations of motion from the Hamilton principle using the matrix-geometric approach is given. Recursive formulas for determining all kinematic and dynamic variables included in the equations are obtained. As an example of a mechanical system with six degrees of freedom, all stages of preparing primary information and compiling equations of motion in the proposed form are demonstrated. Three algorithms are presented that allow resolving the obtained extended system of equations with respect to the generalized velocities and momenta without direct formation of the Hamilton equations. The classification of the equations of motion of rigid body systems is carried out from their structure point of view. The place of the deduced equations in the general classification is also demonstrated. A comparative analysis of the computational complexity of the considered methods for various classes of mechanical systems is carried out. Some diagrams are constructed that allow choosing the most effective modeling method depending on the characteristics of the mechanical system: the number of bodies, the number of degrees of freedom and the structure of the system.

Using Helmholtz"s decomposition theorem, the laws of balance of linear and angular momenta are restated as surface integrals over the closed surface of an arbitrary subregion in a continuum. Newton"s law of action and reaction and Cauchy"s theorem for stress and couple-stress are proved as corollaries of these surface balance laws.

Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models. The model is composed of a univariate Poisson variable, and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component. Two characterizations of this model are shown, first by variance function and then by generalized variance function which is the determinant of the variance function. The latter provides an explicit solution of a particular Monge-Ampère equation.

A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.

The nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time‎. ‎The identification of nonhomogeneous Poisson process relies on the intensity function‎, ‎which can be difficult to determine‎. ‎A straightforward approach is to set the intensity function to a constant value‎, ‎resulting in a homogeneous Poisson process‎. ‎However‎, ‎it is crucial to assess the homogeneity of the intensity function through an appropriate test beforehand‎. ‎Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved‎. ‎In this study‎, ‎we analyzed data on the number of passengers using the Tehran metro‎. ‎Our homogeneity test showed a nonhomogeneous arrival rate of passengers‎, ‎prompting us to explore different functions to estimate the intensity function‎. ‎We considered four functions and used a piecewise function to determine the best intensity function‎. ‎Our findings showed significant differences between the two models‎, ‎highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.