Let Y1, Y2, --Y be ii.d sample from a sub-family of Gamma distributions with 3. density f(y|0) = ye-y//02,y > 0. (i) Find the maximum likelihood estimator of 0. (ii) Find a method of moment cstimator of 0. (ii) Find the asymptotic (large sample) distribution of the MLE obtained in part (i).

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

3

3.
Let Y1, Y2,,Y, be i.i.d sample from a sub-family of Gamma distributions with
density f(y|0) = ye-w/ /0°,y > 0.
(i) Find the maximum likelihood cstimator of e.
(ii) Find a method of moment estimator of 0.
(iii) Find the asymptotic (large sample) distribution of the MLE obtained in part (i).
(iv) Carry out a large sample Wald test for Ho : 0 = 1 v.s. H :0 +1 based on the result in (ii).
Transcribed Image Text:3. Let Y1, Y2,,Y, be i.i.d sample from a sub-family of Gamma distributions with density f(y|0) = ye-w/ /0°,y > 0. (i) Find the maximum likelihood cstimator of e. (ii) Find a method of moment estimator of 0. (iii) Find the asymptotic (large sample) distribution of the MLE obtained in part (i). (iv) Carry out a large sample Wald test for Ho : 0 = 1 v.s. H :0 +1 based on the result in (ii).
Expert Solution
steps

Step by step

Solved in 6 steps

Blurred answer
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON