X5) EXCERSICE Let X₁,..., Xn be a random sample from the inverse Gaussian distribution with pdf 1/2 ƒ(x|µ, X) = (272³) · (2-23) ¹/² -1416-2)²2 e 0 < x <∞. 2 2πχ3 (a) Show that the statistics n = ²X₂ Xi and T = n Σ i=1 X are sufficient and complete. (b) For n = 2, show that X has an inverse Gaussian distribution, nA/T has a x²-1 distribution, and they are independent. (Schwarz and Samanta 1991 do the general case.)

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
i need the answer quickly
X5)
EXCERSICE
Let X₁,..., Xn be a random sample from the inverse Gaussian distribution with pdf
1/2
ƒ (2|µ, X) = (27773) ²
(2²3) ¹/² -460-02²2
e
0 < x <∞0.
2
(a) Show that the statistics
n
= ²1x₂
Xi
and
T =
n
i=1
ΣΧ
X
are sufficient and complete.
(b) For n = 2, show that X has an inverse Gaussian distribution, nA/T has a x²-1
distribution, and they are independent. (Schwarz and Samanta 1991 do the general
case.)
ONC
Transcribed Image Text:X5) EXCERSICE Let X₁,..., Xn be a random sample from the inverse Gaussian distribution with pdf 1/2 ƒ (2|µ, X) = (27773) ² (2²3) ¹/² -460-02²2 e 0 < x <∞0. 2 (a) Show that the statistics n = ²1x₂ Xi and T = n i=1 ΣΧ X are sufficient and complete. (b) For n = 2, show that X has an inverse Gaussian distribution, nA/T has a x²-1 distribution, and they are independent. (Schwarz and Samanta 1991 do the general case.) ONC
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
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