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Confidence intervals for the ratio of scale parameters are constructed in general families of distributions with nuisance (location) parameters. Each of these intervals has coverage probability at least as large as that of the standard minimum size (i.e., minimum ratio of endpoints) interval and, in addition, smaller size. Then analogous improved confidence intervals for the scale parameters subject to order restriction are derived. The method of construction is similar to that in Goutis and Casella [5], [6]. Examples are given and include the normal and exponential distributions as well as the inverse Gaussian distribution which is not a purely location–scale model. Applications to interval estimation of the error variance in variance components models are also discussed.

INTERVAL ESTIMATION FOR THE RATIO OF SCALE PARAMETERS AND FOR ORDERED SCALE PARAMETERS