Types Of Discrete Models Research Articles

On a Class of Discrete Max-Type Difference Equation Model of Order Four

Discrete models are versatile and effective tools for assessing and addressing a wide range of scientific and practical problems. As a type of discrete model, the difference equation model has been widely employed in domains such as algorithm analysis, signal processing, biology, economics, and computer science. The global dynamical behavior of a class of discrete models known as the max-type difference equation model is the subject of the research. The purpose of this work is to look into the behavior of the solution of the following four-order max-type difference equation: z i + 1 = max A i / z i , z i − 3 , i = 0,1,2 , … .

Lattice-Gas-Automaton Modeling of Income Distribution.

A simple and effective lattice–gas–automaton (LGA) economic model is proposed for the income distribution. It consists of four stages: random propagation, economic transaction, income tax, and charity. Two types of discrete models are introduced: two-dimensional four-neighbor model (D2N4) and D2N8. For the former, an agent either remains motionless or travels to one of its four neighboring empty sites randomly. For the latter, the agent may travel to one of its nearest four sites or the four diagonal sites. Afterwards, an economic transaction takes place randomly when two agents are located in the nearest (plus the diagonal) neighboring sites for the D2N4 (D2N8). During the exchange, the Matthew effect could be taken into account in the way that the rich own a higher probability of earning money than the poor. Moreover, two kinds of income tax models are incorporated. One is the detailed taxable income brackets and rates, and the other is a simplified tax model based on a fitting power function. Meanwhile, charity is considered with the assumption that a richer agent donates a part of his income to charity with a certain probability. Finally, the LGA economic model is validated by using two kinds of benchmarks. One is the income distributions of individual agents and two-earner families in a free market. The other is the shares of total income in the USA and UK, respectively. Besides, impacts of the Matthew effect, income tax and charity upon the redistribution of income are investigated. It is confirmed that the model has the potential to offer valuable references for formulating financial laws and regulations.

Bayesian Analysis of Zero-Inflated Distributions

In this paper zero-inflated distributions (ZID) are studied from the Bayesian point of view using the data augmentation algorithm. This type of discrete model arises in count data with excess of zeros. The zero-inflated Poisson distribution (ZIP) and an illustrative example via MCMC algorithm are considered.

Discrete velocity method in the theory of kinetic equations

Abstract A general method of constructing the discrete models for the Boltzmann equation is suggested. This method allows us to get the discrete models which approximate the Boltzmann equation in any bounded domain of the velocity space and preserve the main properties of this equation-the conservation laws and H-theorem. Three different types of discrete models, depending on the kind of the differential collision cross-section, are considered.