let y1 yn be a random sample from a distribution with pdf fy y1 where 0 y is known and 0 a find

Name: let y1 yn be a random sample from a distribution with pdf fy y1 where 0 y is known and 0 a find the maximum likelihood estimator of make sure that you prove that your answer is the mle
Uploaded: 2023-08-03T14:35:09-08:00
Duration: 1 min 27 s
Channel: Dominador Tan
Description: let y1 yn be a random sample from a distribution with pdf fy y1 where 0 y is known and 0 a find the maximum likelihood estimator of make sure that you prove that your answer is the mle

First, we need to write down the likelihood function. The likelihood function is the product of

Question

Let Y1, ..., Yn be a random sample from a distribution with pdf f(y) = (α θ^α)/(y^α+1) where 0 < θ ≤ y, θ is known, and α > 0. a) Find the maximum likelihood estimator of α. (Make sure that you prove that your answer is the MLE.)

          Let Y1, ..., Yn be a random sample from a distribution with pdf
f(y) = (α θ^α)/(y^α+1)
where 0 < θ ≤ y, θ is known, and α > 0.
a) Find the maximum likelihood estimator of α. (Make sure that you prove that
your answer is the MLE.)

Added by Mima

Mathematical Statistics with Applications

Dennis D. Wackerly, William Mendenhall… 7th Edition

Chapter 9

Instant Answer

Solved by Expert Dominador Tan

08/03/2023

Step 1

The likelihood function is the product of the individual probability density functions (pdfs) evaluated at the observed data points. L(α|Y1, ..., Yn) = ∏_{i=1}^{n} f(Yi) = ∏_{i=1}^{n} (α θ^α)/(Yi^α+1) Show more…

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Let Y1, ..., Yn be a random sample from a distribution with pdf f(y) = (α θ^α)/(y^α+1) where 0 < θ ≤ y, θ is known, and α > 0. a) Find the maximum likelihood estimator of α. (Make sure that you prove that your answer is the MLE.)