• Korean Journal of Logic
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• v.15 no.2
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• pp.223-250
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• 2012

The reference-class problem is known as a problem that frequentism on the nature of probability is supposed to encounter. Alan H$\acute{a}$jek argues that other theories on the nature of probability also meet this problem inevitably and claims that we can resolve the problem by regarding conditional probabilities as primitive. In this paper I shall present an adequate way of understanding the reference-class problem and its philosophical implications by scrutinizing his argument. H$\acute{a}$jek's claim is to be classified into the following two: (i) probability is relative to its reference class and (ii) what is known as the 'Ratio' analysis of conditional probability is wrong. H$\acute{a}$jek believes that these two are to be closely related but I believe these two should be separated. Moreover, I shall claim that we should accept the former but not the latter. Finally, regarding the identity condition of reference class I shall distinguish the extensional criterion from the non-extensional one. I shall claim that the non-extensional criterion is the right one for the identity condition of reference class by arguing that the reference-class problem should be regarded as an instance of the qua-problem.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.