Abstract

It is assumed that a population consists of two different types of items, each item being characterized by a random variable called the item's amount. Each type of item may have a different distribution of amounts. Samples are selected from this population so as to contain a fixed total amount rather than a fixed number of items. Some asymptotic properties of the sample amount proportions are derived for the case in which the sampled items have Markov dependence property with respect to type. Estimation of the asymptopic variance is discussed and an application to line of areas is given.

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