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General formulae are developed for the joint probability mass functions and generating functions of (Xn,Sn), (Tr,STr ) (and (Xn,Sn,Fn), (Tr,STr ,FTr )) when Xn belongs to the family of Markov chain ...
Nonparametric estimation of probability density functions, both marginal and joint densities, is a very useful tool in statistics. The kernel method is popular and applicable to dependent data, ...