In this paper, we provide direct evidence that macrophages are a target tissue for leptin. We found that J774.2 macrophages express the functional long form of the leptin receptor and that this becomes tyrosine phosphorylated after stimulation with low doses of leptin. Leptin also stimulates both phosphoinositide 3 kinase (PI 3-kinase) activity and tyrosine phosphorylation of JAK2 and STAT3 in these cells. We investigated the effects of leptin on hormone sensitive lipase (HSL), which acts as a neutral cholesterol esterase in macrophages and is a rate limiting step in cholesterol ester breakdown.In addition, for univariate survival analysis, survival curves were estimated using Laplace Stieltjes transform (LST) of the renewal process. The purpose of this work was to evaluate, by using PolyaAeppli process with PolyaAeppli Rick model, effects of Leptin on hormone sensitive lipase activities using uniform distribution.