Range-Renewal Structure For I.I.D. Model With Non-Pure Type Distribution

Suppose{ξk}k≥1is a sequence of independent and identically distributed random variables, which follows a non-pure type probability law π The range-renewal process of{ξ}k≥1is studied. A series of SLLN are obtained. Furthermore, we prove in this article with mild and natural assumptions on π that, the range-renewal structure of such random sequence almost surely obeys a power law (with a parameter depending on an intrinsic index of the given probability law π).