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.)
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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffaf74cc3-5161-4dde-8bec-a190fad86fff%2F6ff715f9-bedd-4e06-9e0f-ec3f085f758f%2Flyjgyvs_processed.jpeg&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
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 with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
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](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman