Half-Rectified Truncated Distributions: Sampling Theory and Hypothesis Testing

Abstract

In many cases, data are drawn from a population which is distributed approximately normal, but with bounded, rather than infinite, domain. The traditional approach is a truncated normal, but if the population probability approaches zero at the bounds of the domain, serious errors in hypothesis testing may accompany truncation since the tails of the assumed distribution are used in error probability and critical region computation. In this paper, the truncated distribution is transformed so that the abscissa is translated to the truncation points and the curve above the new abscissa is given unit area, and then the curve is half-rectified. The result is a quasi-normal distribution with finite domain yet appearing to retain many properties of the normal. Presented is exact sampling theory, tests of hypothesis methodology, tables of associated probabilities, and illustrations from electronic reliability and oceanography.