On Moments Estimation of the Parameters of a Truncated Bivariate Normal Distribution

Abstract

SUMMARY Explicit expressions for estimators of the parameters of a bivariate normal distribution doubly truncated with respect to both random variables are given in terms of sample moments. These estimators are shown to be con- sistent asymptotically (jointly) normal. A numerical example is included. NATH (1971) has given the maximum likelihood equations for estimating the para- meters of a bivariate normal distribution doubly truncated with respect to both random variables. These equations are nonlinear in the parameters and an iterative method must be used to find the maximum likelihood estimates. In this paper alternate estimators are derived which are considerably easier to compute than the maximum likelihood estimators. These estimators are expressed explicitly in terms of sample moments and are shown to be consistent asymptotically (jointly) normal. In addition, they may be used as a starting vector for solving the maximum likelihood equations and should, in general, reduce the number of cycles