Sample Size Required to Estimate the Parameter in the Uniform Density withindUnits of the True Value

Abstract

A two-step procedure is given to find the sample size necessary to estimate the parameter θ in the uniform density within d units of the true value. It is demonstrated that an exact solution for all values of θ doesn't exist based on the maximum likelihood estimator. A table is presented which can be used to find the second sample size, n , such that P [| y n − θ | < d ] > 1− α is true, where Y n is the largest observation in the second sample, for 1 − α = .90, .95, .99 and the preliminary sample size m = 2, 5 (5) 30 (10) 50 (25) 100. Also a table of comparisons between the expected sample size in this paper and two other solutions is given.