Order Statistics Based on a Combined Simple Random Sample from a Finite Population and Applications to Inference

In this paper, we study probability distributions of order statistics from a set obtained by combining several simple random samples (SRS) selected from the same finite population. Each simple random sample is taken using without replacement selection procedure and does not contain any ties. On the other hand, in the combined sample, the same observation may appear more than once since each SRS is selected from the same finite population. Consequently, the number of the distinct observations in the combined sample is a discrete random variable. We provide the probability mass function of this discrete random variable. Next, using the order statistics in the combined SRSs, we construct confidence intervals for the quantiles and outer-inner confidence intervals for the quantile interval of a finite population. Finally, we also present a prediction interval for a future observation from the same finite population.