The Asymptotic Variance of the Estimated Proportion Truncated from a Normal Population

Abstract

Cohen (1959, 1961) has derived simplified maximum likelihood estimators of the parameters μ and σ of a truncated normal distribution, as well as the asymptotic covariance matrix of the parameter estimates. In certain applications we need to estimate the proportion truncated or the reciprocal of this proportion and would like to know the variances of these estimates. In this paper we derive asymptotic variances for the above estimates and present the results of a simulation study which examines the rate of convergence of these variances to the asymptotic values.

KEY WORDS:

• Asymptotic variance
• Maximum likelihood estimation
• Truncated normal distribution