Mathematics – Probability
Scientific paper
2003-05-02
Statistical Methods, Vol. 5 (2), December-2003, 126-139
Mathematics
Probability
14 pages, in journal format. In the first sentence of the last paragraph on page 131 the part after the second comma was inadv
Scientific paper
Continuing the study reported in Satheesh (2001),(math.PR/0304499 dated 01 May 2003) and Satheesh (2002)(math.PR/0305030 dated 02May 2003), here we study generalizations of infinitely divisible (ID) and max-infinitely divisible (MID) laws. We show that these generalizations appear as limits of random sums and random maximums respectively. For the random sample size N, we identify a class of probability generating functions. Necessary and sufficient conditions that implies the convergence to an ID (MID) law by the convergence to these generalizations and vise versa are given. The results generalize those on ID and random ID laws studied previously in Satheesh (2001b, 2002) and those on geometric MID laws studies in Rachev and Resnick (1991). We discuss attraction and partial attraction in this generalization of ID and MID laws.
Sandhya E.
Satheesh S.
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