S(z|4, A) = () the statistics `X and 1=E in ent and complete. , show that X has an inverse Gaussian distributio on, and they are independent. (Schwarz and Samanta

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Let X1,...,Xn be a random sample from the inverse Gaussian distribution with pdf
f(z|4, A) =
1/2 -A(-)?
e , 0<I< 0o.
(a) Show that the statistics
X and T= n
are sufficient and complete.
(b) For n = 2, show that X has an inverse Gaussian distribution, nA/T has a x-1
distribution, and they are independent. (Schwarz and Samanta 1991 do the general
case.)
Wi
Transcribed Image Text:Let X1,...,Xn be a random sample from the inverse Gaussian distribution with pdf f(z|4, A) = 1/2 -A(-)? e , 0<I< 0o. (a) Show that the statistics X and T= n are sufficient and complete. (b) For n = 2, show that X has an inverse Gaussian distribution, nA/T has a x-1 distribution, and they are independent. (Schwarz and Samanta 1991 do the general case.) Wi
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