Question 3. Let X1,···, Xn be a sample from the pmf Po(X = x) = α(x)0x f(0) x = 0,1,2,. " where 0 > 0, α(x) > ·0, ƒ (0) = Σa(x)0x, α(0) = 1, and let T = T(X1,···, Xn) = X. Write i=1 x = n c(t,n) = Σ П α(xi), ЄR(t) i=1 where (x1,,xn) and R(t) = {(x1,xn) EN T(x1,,xn) = t}. Show that T is a complete sufficient statistic for 0, and that the UMVUE for d(0) = 0" (r > 0 is an integer) is given by 0, if t < r, Y₁(t) = c(t,n) " c(t-r,n) if t≥ r . iid Using this result find the UMVUE of 0 when Xi ~ Poisson(0).
Question 3. Let X1,···, Xn be a sample from the pmf Po(X = x) = α(x)0x f(0) x = 0,1,2,. " where 0 > 0, α(x) > ·0, ƒ (0) = Σa(x)0x, α(0) = 1, and let T = T(X1,···, Xn) = X. Write i=1 x = n c(t,n) = Σ П α(xi), ЄR(t) i=1 where (x1,,xn) and R(t) = {(x1,xn) EN T(x1,,xn) = t}. Show that T is a complete sufficient statistic for 0, and that the UMVUE for d(0) = 0" (r > 0 is an integer) is given by 0, if t < r, Y₁(t) = c(t,n) " c(t-r,n) if t≥ r . iid Using this result find the UMVUE of 0 when Xi ~ Poisson(0).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text:Question 3.
Let X1,···, Xn be a sample from the pmf
Po(X = x)
=
α(x)0x
f(0)
x = 0,1,2,.
"
where 0 > 0, α(x) > ·0, ƒ (0) = Σa(x)0x, α(0) = 1, and let T = T(X1,···, Xn) =
X. Write
i=1
x =
n
c(t,n) = Σ П α(xi),
ЄR(t) i=1
where (x1,,xn) and R(t) = {(x1,xn) EN T(x1,,xn) = t}. Show
that T is a complete sufficient statistic for 0, and that the UMVUE for d(0) = 0" (r >
0 is an integer) is given by
0,
if t < r,
Y₁(t) =
c(t,n)
"
c(t-r,n) if t≥ r .
iid
Using this result find the UMVUE of 0 when Xi
~
Poisson(0).
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman