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