By Marcus R.

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**Extra info for A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution**

**Example text**

This limit relation holds because of the following estimates: kn ]log(l'1"~4)(x') K sup l(jgkn ~" 11 - ~ n j ( X ' ) ~ k~ - log e ( ~ n j ) ( x ' ) [ I1 - ^ pnj (x')1 i= 4 h f and k. n )J ( B + c) k,. 9 Theorem. ,k n be array of probability measures on E+. Let further F be a Radon measure on E+ with inf(1,1xlP)F(dx)

S. convergence of ~ the ~Yk" If T = IR+ and if all measures ~t are concentrated on E+ then we have for every constant c>o and tp s ~ o ~,. qxl p ~t(dx) =~ Ln,,u,c] llx+YllP~s(dX)~t_s(dY)~ ~ ~x~ p ~s(dX). u,~U,c3 Hence we get lira sup~ "'~ if Nx~ p ~ s ( d X ) ~ s~r [i~U~-3 l~xl~ p ~ r ( d X ) ~ . U>"] Since = I "xUPP~'(~'~=4Yk)(dx) the LP-convergence of the series ~ ~Yk now follows. I Remarks. I. Let (X,~',~) be a measure space, and let G be the Banach lattice of all bounded 7-_measurable functions.

The canonical imbedding of F~ into F ~ and the canonical projection of F ~ onto F~ Y resp. On the set algebra y~ we can define the set function ~ in setting ~(A):= ~ ( B ) if B~(F~) and A=~-I(B). e. we have defined our probability space (~,~,P). 3S T(y~... For all y~S we now put ~y := Then we have surely ~y(P! ,yn)s ~H the sequence (~Yi)iGi~n is independent. e. (i) and (ii) are satisfied. Now suppose that the additional assumptions of the theorem hold. A ~-~yk + ~ y - ~ y k for any sequence (yn) in S such that (YI'''''Yn)~ ~ for all n and K y = sup~=4 Yke S.

### A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution by Marcus R.

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