Let Y1, Y2, . . . , Yn denote a random sample of
Chapter 9, Problem 28E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample of size \(n\) from a Pareto distribution (see Exercise 6.18). Then the methods of Section 6.7 imply that \(Y_{(1)}=\min \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\) has the distribution function given by
\(F_{(1)}(y)=\left\{\begin{array}{lc}0, & y \leq \beta \\1-(\beta / y)^{an}, & y>\beta\end{array}\right\}\)
Use the method described in Exercise 9.26 to show that \(Y_{(1)}\) is a consistent estimator of \(\beta\).
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