Let Y1, Y2, . . . , Yn denote independent and identically
Chapter 9, Problem 44E(choose chapter or problem)
Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote independent and identically distributed random variables from a Pareto distribution with parameters \(\alpha \text { and } \beta\). Then, by the result in Exercise 6.18, if \(\alpha, \beta>0\),
\(f(y \mid \alpha, \beta)=\left\{\begin{array}{ll} \alpha \beta^{\alpha} y^{-(\alpha+1)}, & y \geq \beta \\ 0, & \text { elsewhere } \end{array}\right.\)
If \(\beta\) is known, show that \(\prod_{i=1}^{n} Y_{i}\) is sufficient for \(\alpha\)
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
\alpha \text and \beta
\alpha, \beta>0
\(f(y \mid \alpha, \beta)={ \alpha \beta^\alpha y^-(\alpha+1), & y \geq 0, elsewhere
\beta
\prod_i=1^n Y_i
\alpha
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