Strassen's LIL for the Lorenz curve

JOURNAL OF MULTIVARIATE ANALYSIS

卷:59

Article

关键词: Lorenz curve;    Lorenz process;    Strassen's law of the iterated logarithm;    Vervaat process;    integrated empirical difference process;    empirical process;    quantile process;    relative compactness;    mean residual life process;    total time on test function;    Lorenz process of order nu;    Shannon process;    redundancy process;   

DOI  :  10.1006/jmva.1996.0050

来源: Elsevier

【 摘 要 】

We prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying distribution Function F and its inverse F-1 are continuous, and the moment EX(2+epsilon) is finite for some epsilon>0. Previous work in this area is based on assuming the existence of the density f:= F' combined with Further assumptions on F and f: Being based only on continuity and moment assumptions, our method of proof is different from that used previously by others, and is mainly based on a limit theorem for the (general) integrated empirical difference process. The obtained result covers all those we are aware of on the LIL problem in this area. (C) 1996 Academic Press, Inc.

【 授权许可】

Free