Outer and Inner Confidence Intervals Based on Extreme Order Statistics in a Proportional Hazard Model

Let Mi and M0 i be the maximum and minimum of the ith sample from k independent sample with different sample sizes, respectively. Suppose that the survival distribution function of the ith sample is ¯ Fi = ¯ Fi, where i is known and positive constant.It is shown that how various exact non-parametric inferential procedures can be developed on the basis of Mi’s and M0 i ’s for distribution function F without any assumptions about it other than F is continuous. These include outer and inner confidence intervals for quantile intervals and upper and lower confidence limits for quantile differences. Three schemes have been investigated and in each case, theassociated confidence coefficients are obtained. A numerical example is given in order to illustrate the proposed procedure.