et A1, A2,..., An be lid random variables from a Pareto distribution, with caf (x; α) A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is an = ܕ ܡ n In X₁ C. Construct an estimator T(ân) such that E(T (ân)) =a. Is it a best estimator for a? 3 " 21 V

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
100%

CAN DO TYPEWRITTEN FOR UPVOTE?

2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0.
A. Find the Cramer-Rao lower bound for estimators of a.
B. Show that the MLE for a is an
n
Σ', la XT
C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?
Transcribed Image Text:2. Let X₁, X2,..., Xn be iid random variables from a Pareto distribution, with cdf F(x; a) = 1-xa, x ≥ 1, a > 0. A. Find the Cramer-Rao lower bound for estimators of a. B. Show that the MLE for a is an n Σ', la XT C. Construct an estimator T(ân) such that E(T(ân)) = a. Is it a best estimator for a?
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman