Some applications of ratios of normal random variables require both the numerator and denominator of the ratio to be positive if the ratio is to have a meaningful interpretation. In these applications, there may also be substantial likelihood that the variables will assume negative values. An example of such an application is when comparisons are made in which treatments may have either efficacious or deleterious effects on different trials. Classical theory on ratios of normal variables has focused on the distribution of the ratio and has not formally incorporated this practical consideration. When this issue has arisen, approximations have been used to address it. In this article, we provide an exact method for determining (1 ?alpha) confidence bounds for ratios of normal variables under the constraint that the ratio is composed of positive values and connect this theory to classical work in this area. We then illustrate several practical applications of this method.
This article appears as:
Ennis, D., Ennis, J., Palen, J., Lampe, R. (2008). Confidence bounds for positive ratios of normal random variables. Communications in Statistics - Theory and Methods, 37(3), 307-317.
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Confidence bounds for positive ratios of normal random variables
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