The kin number problem in a multitype Galton-Watson population.
"The kin number problem in its simplest form is that of the relationship between sibship sizes and offspring numbers.... Further studies have been made, concerning relatives of other degrees of affinity than siblings, but these did not usually yield joint distributions.  Recently this aspect of the problem has been studied in the framework of a Galton-Watson process.... In these studies the population is treated as monotype.  Applications such as pedigree studies of diseases require a multitype approach (in the example, two types:  victims and others).  In this paper such a study is undertaken."  Problems and questions involved in this type of approach are discussed, and joint distributions are obtained under a number of sampling schemes.
Joffe
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Waugh Wao
D003710:Demography; D004194:Disease; D004812:Epidemiologic Methods; D005191:Family Characteristics; D005195:Family Relations; D008962:Models, Theoretical; D012106:Research; D013223:Statistics as Topic
Data Analysis; Demographic Analysis; Diseases; Epidemiologic Methods; Family And Household; Family Characteristics; Family Relationships; Family Size; Mathematical Model; Models, Theoretical; Research Methodology; Statistical Studies; Studies