UPPER AND LOWER-BOUND DISTRIBUTIONS THAT GIVE SIMULTANEOUS CONFIDENCE-INTERVALS FOR QUANTILES

We propose a new method far constructing parametric confidence interva ls for quantiles of an unknown distribution. These confidence interval s are constructed so that the joint probability that all intervals sim ultaneously contain their respective percentiles is at least a preset value. Thus we may also use the set of either upper or lower confidenc e limits to define an upper (or lower) bound distribution function, wh ich we call an upper (or lower) tolerance distribution because this di stribution may also be used to construct tolerance intervals for the u nknown distribution. We derive tolerance distributions with exact cove rage probability for lid samples from distributions in the location-sc ale family. Tolerance distributions can also be used for best- and wor st-ease analyses, as we illustrate by considering bounds on the distri bution of the time interval between the onset of infectiousness and de velopment of detectable antibody in individuals newly infected with th e human immunodeficiency virus (HIV), the virus that causes acquired i mmune deficiency syndrome (AIDS).