Laws of populations formation on territories.

Quantile model of accumulation for the description of the quantitative laws inherent in a population of territories is considered in the article. This mathematical model is based on conceptof growing system, which is described by formula: j 1 j j ( j ), Qk Qk zk gk Qk - = where k is a number of territory, j - number of period, j zk are independent by j, equally distributedpositive random values, gk (x) - some functions, which would be chosen according to mechanism of accumulation.The growing system is understood as any set of objects of one nature participating in processesof origin, formation and development of the system, submitted to defined laws, same for all objects.Lognormal model, as a special case of Kapteyns distribution, and methods of models applicationto demographic researches are considered in detail. Examples of application of this modelare adjusted to research of distributions laws of the population on subjects and federal districtsof the Russian Federation, and also the analysis of distribution of population of the USA in variousyears is carried out, since 1930 and finishing 2000.Regression dependency of logarithm of territories population on the quantiles of the normallaw is considered. In many respects results of researches confirm expediency of the lognormallaw's application at the description of a population's distribution. Its illustrated that in due courseof time a formed population of states of the USA is approximated by linear regression much better.

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