Simulation and Robust Modifications of Estimates in Branching Processes

This study is focused on the comparison and modification of different estimates arising in the branching processes. Simulations of models with or without migration are put through. Due to the complexity of the computations the algorithms are designed with the language of technical computing MATLAB. Using the simulations, estimates of the o spring mean of the generated processes are calculated. It is well known in the literature that under certain conditions the asymptotic distribution of the estimates is proved to be normal. Using the asymptotic normality a modified method of maximum likelihood is proposed. The aim is to obtain trimmed maximum likelihood estimates based on several sample paths with the same number of generations. Thus in a natural way the observations, inconsistent with the aprior information about the asymptotic normality are excluded from the model. The computation of the standard error allows the comparison of different types of estimates.

Classification of Chenopodium Genus Populations and Species Based on Continuous and Categorical Variables

2000 Mathematics Subject Classification: 62P10, 62H30

Comparing Several Methods of Discriminant Analysis on the Case of Wine Data

2000 Mathematics Subject Classification: 62H30, 62J20, 62P12, 68T99

Approaches to Organization of Teaching for Creating Digital Learning Materials

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Computer Mathematics for Motivated Students

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Group Work as a Strategy to Improve the Effectiveness of the Learning Process

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.