THE SINGLY TRUNCATED NORMAL DISTRIBUTION: A NON-STEEP EXPONENTIAL FAMILY

JOAN DEL CASTILLO

Department of Mathematics, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

(Received September 17, 1992; revised January 21, 1993)

Abstract. This paper is concerned with the maximum likelihood estimation problem for the singly truncated normal family of distributions. Necessary and suficient conditions, in terms of the coefficient of variation, are provided in order to obtain a solution to the likelihood equations. Furthermore, the maximum likelihood estimator is obtained as a limit case when the likelihood equation has no solution.

Key words and phrases: Truncated normal distribution, likelihood equation, exponential families.