The singly truncated normal distribution: A non-steep exponential family

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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. © 1994 The Institute of Statistical Mathematics.
Original languageEnglish
Pages (from-to)57-66
JournalAnnals of the Institute of Statistical Mathematics
Publication statusPublished - 1 Mar 1994


  • Truncated normal distribution
  • exponential families
  • likelihood equation


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