Question

Let X1, X2, .... , Xn constitute a random sample from a population X with the following pdf f(x; x0, ?) = ? x0^? x^-?-1 x ? x0, ? > 1 (a) Use the method of maximum likelihood estimation to find an estimate for ?, if possible. (b) Why the MLE, if exists, is guaranteed to be the best estimator.

          Let X1, X2, .... , Xn constitute a random sample from a population X with the following
pdf
f(x; x0, ?) = ? x0^? x^-?-1     x ? x0, ? > 1
(a) Use the method of maximum likelihood estimation to find an estimate for ?, if
possible.
(b) Why the MLE, if exists, is guaranteed to be the best estimator.

Let X1, X2, .... , Xn constitute a random sample from a population X with the following
pdf
f(x; x0, ?) = ? x0^? x^-?-1 x ? x0, ? > 1
(a) Use the method of maximum likelihood estimation to find an estimate for ?, if
possible.
(b) Why the MLE, if exists, is guaranteed to be the best estimator.

Added by Paul A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Anna D.

Step 1

We have independent observations X1,...,Xn from the Pareto-type pdf f(x; x0, θ) = θ x0^θ x^{-(θ+1)} for x ≥ x0, with parameter θ > 1 and known x0. The joint density (likelihood) is defined only when all Xi ≥ x0; otherwise the likelihood is 0. Show more…

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Let X1, X2, ..., Xn constitute a random sample from a population X with the following pdf: f(x; x0, θ) = θ x0^θ x^-θ-1, x ≥ x0, θ > 1 (a) Use the method of maximum likelihood estimation to find an estimate for θ, if possible. (b) Why the MLE, if exists, is guaranteed to be the best estimator.