(Solution) - Suppose that X1 Xm form a -(2025 Original AI-Free Solution)
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Suppose that X1, . . . , Xm form a random sample of m observations from a continuous distribution for which the p.d.f. f (x) is unknown, and that Y1, . . . , Yn form an independent random sample of n observations from another continuous distribution for which the p.d.f. g(x) is also unknown. Suppose also that f (x) = g(x ? ?) for ?? < x , where the value of the parameter ? is unknown (?? < ? < ?). Let F?1 be the quantile function of the Xi ?s, and let G?1 be the quantile function of the Yj ?s. Show that F?1(p) = ? + G?1(p) for all 0 < p < 1.