On the Efficiency of Ban Estimates of the Parameters of Normal Populations Based on Truncated Samples

Abstract

Summary

It is shown that when estimating tbe mean μ of a normal population, the standard deviation σ being known. the BAN estimate of μ based on a truncated sample of size n is less efficient than that based on a complete sample of the same size whatever be the point of truncation x_a. On the contrary, when estimating σ alone μ being known, the BAN estimate of σ based on the truncated sample is substantially more efficient than that based on the complete sample whenever x_a>μ in the case of left truncation, and x_a<μ in the case of right truncation.