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Extra resources for Accuracy of MSI testing in predicting germline mutations of MSH2 and MLH1 a case study in Bayesian m

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He proved the answer to this quest- ion in the affirmative by utilizing the following result. 1. Let R(t) be a r e a l v a l u e d f u n c t i o n o f bounded v a r i a t i o n normegative real line. Let G(x) be a d i s t r i b u t i o n G(x) > 0 f o r a l l x > 0. on t h e f u n c t i o n such t h a t G(0+) = 0 and Assume t h a t +co (11) f G(t-x)dR(t) = 0 , 0 x >- 0 , and t h a t t h e L a p l a c e t r a n s f o r m +co G*(s) = f e-SXdG(x) -co does n o t v a n i s h f o r Res ~> 0. O u t l i n e of p r o o f : Rl(t) = R(t) identically Then R(t) i s c o n s t a n t f o r t > 0.

Letting u ÷ 0 we get F(y) = 1-e -y , y > 0, which was to be proved. Let us turn to question (ii). There are only a few solutions to this problem under rather restrictive assumptions. Some of these solutions, however, are very valuable in engineering applications. Namely, several failure models can be approx- imated by a model in which the components are independent (but not identically distributed). For such models, however, the asymptotic extreme value distributions are of monotonic hazard rate (see J.

2. A stability theorem As it was already indicated in Chapter i, the subject matter of the theory of characterizations is to show that only one distribution (which may contain one or several parameters) can satisfy a set of specific properties. In most applications, however, statistical or mathematical properties can be verified only approximately. The question thus arises whether several different distributions can be the result of an investigation if a property is slightly modified. called the stability theory of characterizations.

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