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:

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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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