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The aim of the paper is to describe a model of the development of the Covid-19 contamination of the population of a country or a region. For this purpose a special branching process with two types of individuals is considered. This model is intended to use only the observed daily statistics to estimate the main parameter of the contamination and to give a prediction of the mean value of the non-observed population of the contaminated individuals. This is a serious advantage in comparison with other more complicated models where the observed official statistics are not sufficient. In this way the specific development of the Covid-19 epidemics is considered for different countries.

The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily statistics to estimate the main parameter of the infection and to give a prediction of the mean value of the non-observed population of the infected individuals. Similar problems are considered also in the case when the processes admit an immigration component. This is a serious advantage in comparison with other more complicated models where the officially reported data are not sufficient for estimation of the model parameters. In this way the specific development of the Covid-19 epidemics is considered also for all countries as it is given in the specially created site http://ir-statistics.net/covid-19 where the obtained results are updated daily., Comment: arXiv admin note: substantial text overlap with arXiv:2004.00941

It is well known that the estimation of the parameters of branching processes (BP) as an important issue used for studying and predicting their behavior needs lots of energy consuming work and faces many computational difficulties. The task is even more complicated in the presence of outliers − "wrong", "untypical" or "contaminated" data, which require a different statistical approach. The existing asymptotic results for the classical estimators can be combined with a generic method for constructing robust estimators, based on the trimmed likelihood and called weighted least trimmed estimators (WLTE). Despite the computational intensity of the procedure it gives well interpretable results even in the case of minor a priori satisfied asymptotic requirements. In the paper we explain the main outlines of this routine and show some classical estimators and their robust modifications in the important class of discrete-time branching processes with immigration. We present a software package for MATLAB for simulation, plotting and estimation of the process parameters. The package is available on the Internet, under the GNU License., 2010 Mathematics Subject Classification: 60J80.

The objective of this report is to document the process and summarize the results from the second phase of the pilot implementation of statistical models for measuring the value-added of Bulgarian schools through analysis of the national student’ assessments results. This report presents the technical aspects of the pilot and the key outcomes in terms of value-added measure for each of the schools included in the analysis. It is intended to ensure the institutional memory for the pilots and to stimulate the discussions at technical level among experts and decision makers at the Ministry of Education and Science (MES), focusing on the relevance and applicability of the piloted statistical models, in the context of Bulgaria student assessment framework, and given the available data. The report documents all the data processing, adjustments, and procedures run as part of the school value added modeling.

The paper deals with a parametric estimation in branching processes {Zt(n)} having random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family - the class of the power series offspring distributions. Consistency and asymptotic normality of the estimators are obtained for all values of the offspring mean m, 0, 2000 Mathematics Subject Classification: 60J80, 62M05, Partialy supported by Pro-ENBIS GTC1 -2001-43031. The paper is supported by the National Science Fund of Bulgaria, Grant No. MM-1101/2001.

In the present paper we consider the discrete time branching process with immigration and its relationship to the Bienayme-Galton-Watson process with a random number of ancestors. Several estimators of the offspring mean are considered - the Harris estimator, the conditional least squares estimator of Heyde-Seneta, the conditional weighted least squares estimator of Wei-Winnicki and the estimator of Dion and Yanev. Their properties are compared using computational results based on simulations of the entire immigration family trees. The asymptotic normality of the estimator of Dion and Yanev is combined with the general idea of the trimmed and weighted maximum likelihood. As a result, robust modifications of the offspring mean estimator is proposed., 2000 Mathematics Subject Classification: 60J80., The paper is partially supported by the National Science Fund of Bulgaria, Grant No VU-MI-105/2005.

The objective of this report is to describe the process and summarize the results from the pilot implementation of statistical models for measuring the value-added of Bulgarian schools through analysis of the national student’ assessments results. This report presents the technical aspects of the pilot and the key outcomes in terms of value-added measure for each of the schools included in the analysis. The report documents all data processing, adjustments, and procedures run as part of the school value added modeling and in this respect, it is also intended expert statisticians and researchers. The national student assessment results in Bulgaria are reported on a non-transformed raw point scale accompanied by a table that allows a transformation of the raw points to the six-grade rating scale, adopted for measuring students’ performance. Based on this, each school receives an average score and some means of comparison with other schools in the country. Analyzing the test results through value-added analysis is a new approach for the country and the findings from this pilot are intended to inform policy makers in Bulgaria about the advantages and limitations of value-added measures (VAMs) in the context of the Bulgarian education system, its student assessment framework, and the data collected and used by the education management information system.

2000 Mathematics Subject Classification: 60J80., The paper deals with a robust parametric estimation in branching processes {Zt(n)} having a random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family – the class of the power series offspring distributions. Robust estimators, based on one and several sample paths, are proposed and studied for all values of the offspring mean m, 0 < m < ∞, in the subcritical, critical and supercritical case., The paper is partially supported by grant MM-1101/2001 of the NFSI – Bulgaria.

The paper is supported in part by the National Science Fund of Bulgaria, Grant No VU-MI -105/2005 and by ECO-NET 06 action 12634TJ founded by French Foreign Office., In the present paper we consider the branching process with immigration and its relationship to the Bienayme - Galton - Watson process with a random number of ancestors. Several estimators of the immigration component are considered - the conditional least squares estimator of Heyde - Seneta, the conditional weighted least squares estimator of Wei - Winnicki and the estimator of Dion and Yanev. Their comparison is based on simulations of the entire immigration family trees and computational results. The asymptotic normality of the estimator of Dion and Yanev is combined with the general idea of the trimmed and weighted maximum likelihood. As a result, robust modifications of the immigration component estimator is proposed. They are based on one and several realizations of the entire family tree and are studied via simulations and numerical results., 2000 Mathematics Subject Classi cation: 60J80.