By Yasui Y.

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**Extra resources for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono**

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We will, however, give a rather simple direct proof. 29 Proof Assume that H is not ergodic. It follows from lemma 4 (iv) that there exist ~ ( 0 , 1 ) and two strictly stationary H I and ~2 with H I r H 2 such that H = aH I @ (I - ~)H 2. From the definition of PH it follows that PH = ~PH I + (I - ~)PH2. PH 2 From theorem 4 it follows that PHI and are stationary and from theorem I that PHI # PH 2 . Thus, using lemma 4 (iv) again it follows that PH is not ergodic. Assume now that H is ergodic. Let B I and B 2 be two arbitrary sets in A(M) a n d l e t n o be such that B 1 a n d B2 b e l o n g s to Bn (M).

N. We may observe that for a weighted Poisson process N, we have Pr{N(t) = 0} = f e -xt U{dx), 0 which, considered as a function of t, is the L a p l a c e - t r a n s f o r m of U. Thus Pr{N(t) = 0} for t ~ 0 determines U uniquely and thus the distribution of N. 5. If on the other hand for some point process {N(t) ; t > 0} oo Pr{N(t) = n) = f (xt)~n e -xt U{dx} 0 for all t > 0 and n = 0,1,2,... and some distribution point process need not be a weighted Poisson process. berg (1969, p 123) gives an example.

Assume that E Ak{B} < ~ for all bounded B ~ B ( X ) . ,Jm} m=1 m {J1 .... ,k} into m disjoint non-empty sets. The following theorem will be of some importance. 25 Theorem 6 For all bounded B I , B 2 @ B ( X ) the random variables N{B I} - A{B I} and A{B 2} are uncorrelated. There exist, however, BI,B 2 ~ B ( X ) such that N{B I} - A{B I} and A{B 2} are dependent unless N is a Poisson process. Further N{B I} - A{B 1} and N{B 2} - A{B 2} are uncorrelated for all bounded and disjoint BI,B 2 ~ B ( X ) .

### A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono by Yasui Y.

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