Asymptotics for self-normalized random products of sums of i.i.d. random variables |
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| Authors: | Tian-Xiao Pang Zheng-Yan Lin |
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| Institution: | a Department of Mathematics, Zhejiang University, Hangzhou 310027, China
b Research Institute of Natural Science, Geongsang National University, Jinju 660-701, Republic of Korea |
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| Abstract: | Let  be a sequence of independent and identically distributed positive random variables, which is in the domain of attraction of the normal law, and tn be a positive, integer random variable. Denote  ,  , where  denotes the sample mean. Then we show that the self-normalized random product of the partial sums,  , is still asymptotically lognormal under a suitable condition about tn. |
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| Keywords: | Self-normalized Products Domain of attraction of the normal law Lognormal distribution I i d random variables |
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