Estimation of parameters under random determinations on each unit of a random sample

Abstract

When there are several determinations per unit of a sample and j, the number of determinations is a random variable, the mean of the means per unit can be taken to be an unbiased estimate of the population mean. The variance of the estimate and the estimate of this variance is derived under general conditions. Since the expressions involve E(1/j) in particular situations where E (1/j) may be calculated and tabled, they may be evaluated with the he!p of the tables given. These results may also be extended to other situations suitably.