Maximum Likelihood Estimation of the Parameters of a Normal Distribution which is Truncated at a Known Point

Abstract

1. Introduction. The two cases where a normal distribution is “truncated” at a known point have been treated by R. A. Fisher (1) and W. L. Stevens (2), respectively. Fisher treated the case in which all record is omitted of observations below a given value, while Stevens treated the case in which the frequency of observations below a given value is recorded but the individual values of these observations are not specified. In both cases the distribution is usually termed truncated. In the first case, admittedly, the observations form a random sample drawn from an incomplete normal distribution, but in the second case we sample from a complete normal distribution in which the obtainable information in a sense has been censored, either by nature or by ourselves. To distinguish between the two cases the distributions will be called truncated and censored 1 The term “censored” was suggested to me by Mr J. E. Kerrich. , respectively. The term “point of truncation” will be used for both.