Strassen's LIL for the Lorenz Curve
We prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying distribution functionFand its inverseF-1are continuous, and the momentEX2+[var epsilon]is finite for some[var epsilon]>0. Previous work in this area is based on assuming the existence of the densityf:=F' combined with further assumptions onFandf. 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.
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Volume (Year): 59 (1996)
Issue (Month): 1 (October)
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