Compound Poisson and signed compound Poisson approximations to the Markov binomial law

Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are calculated. For the upper bounds, the smoothing properties of compound Poisson distributions are applied. For the lower bound estimates, the characteristic function method is used.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ246 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Compound Poisson approximation

We overview the results on the topic of compound Poisson approximation to the distribution of a sum Sn=X1+⋯+Xn of (possibly dependent) random variables. We indicate a number of open problems and discuss directions of further research

Compound Poisson approximation

We overview the results on the topic of compound Poisson approximation to the distribution of a sum Sn=X1+⋯+Xn of (possibly dependent) random variables. We indicate a number of open problems and discuss directions of further research

Family time, parental behaviour model and the initiation of smoking and alcohol use by ten-year-old children: an epidemiological study in Kaunas, Lithuania

BACKGROUND: Family is considered to be the first and the most important child development and socialization bond. Nevertheless, parental behaviour model importance for the children, as well as family time for shared activity amount influence upon the child's health-related behaviour habit development has not been yet thoroughly examined. The aim of this paper is to indicate the advanced health-hazardous behaviour modelling possibilities in the families, as well as time spent for joint family activities, and to examine the importance of time spent for joint family activities for the smoking and alcohol use habit initiation among children. METHODS: This research was carried out in Kaunas, Lithuania, during the school year 2004–2005. The research population consisted of 369 fifth-grade schoolchildren (211 (57.2%) boys and 158 (42.8%) girls) and 565 parents: 323 (57.2%) mothers and 242 (48.2%) fathers. The response rate was 80.7% for children; 96.1% and 90.6% for mothers and fathers correspondingly. RESULTS: Eating a meal together was the most frequent joint family activity, whereas visiting friends or relatives together, going for a walk, or playing sports were the most infrequent joint family activities. More than two thirds (81.5%) of parents (248 (77.0%) mothers and 207 (85.9%) fathers (p < 0.05)) reported frequenting alcohol furnished parties at least once a month. About half of the surveyed fathers (50.6%) together with one fifth of the mothers (19.9%) (p < 0.001) were smokers. More frequently than girls, boys reported having tried smoking (6.6% and 23.0% respectively; p < 0.001) as well as alcohol (31.16% and 40.1% respectively; p < 0.05). Child alcohol use was associated both with paternal alcohol use, and with the time, spent in joint family activities. For instance, boys were more prone to try alcohol, if their fathers frequented alcohol furnished parties, whereas girls were more prone to try alcohol, if family members spent less time together. CONCLUSION: Joint family activity time deficit together with frequent parental examples of smoking and alcohol use underlie the development of alcohol and smoking addictions in children to some extent. The above-mentioned issues are suggested to be widely addressed in the comprehensive family health education programs

Compound Poisson approximation

Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, and more. Compound Poisson Approximation synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems, and exercises, it will become the standard reference book on the topic. Features • Provides a comprehensive overview of this rapidly expanding field • Synthesizes the most important research results of recent years • Presents an array of special topics • Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics