Solved: Let Y1, Y2, . . . , Yn denote a random sample of
Chapter 8, Problem 15E(choose chapter or problem)
Let \(\mathrm{Y}_{1}, \mathrm{Y}_{2}, \ldots, \mathrm{Y}_{\mathrm{n}}\) denote a random sample of size n from a population whose density is given by
\(f(y)=\left\{\begin{array}{ll} 3 \beta^{3} y^{-4}, & \beta \leq y \\ 0, & \text { elsewhere } \end{array}\right.\)
Where \(\beta>0\)is unknown. (This is one of the Pareto distributions introduced in Exercise 6.18.)
Consider the estimator \(\widehat{\beta}=\min \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\)
Derive the bias of the estimator \(\widehat{\beta} .\)Derive MSE \((\widehat{\beta})\)
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
f(y)=3 \beta^3 y^-4, & \beta \leq y\ 0, &elsewhere
\beta>0
widehat\beta=\min(Y_1, Y_2, \ldots, Y_n\right)
widehat\beta .\)
(\widehat\beta)
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