Estimating Distributions using the Theory of Relative Increment Functions

Abstract

Bounded growth processes can be modelled, approximately by different mathematical models. The challenge for statisticians and mathematicians is finding suitable models for these processes. In this paper we illustrate a non-parametric method, using the the theory of relative increment functions, of estimating density functions of these processes. For a long time, mathematicians attempted to describe the cumulative prevalence of caries with the assumption that there is a mathematical model that would describe the caries prevalence and may be used for predicting caries incidences. In 1960 Porter and Dudman [12] introduced The relative increment function and called it the relative increment of decay as they designed it to compare dental caries increments among children. Further studies of this led to the motivation that the best suitable model for describing the cumulative prevalence of caries should be chosen from a set of distributions that have relative increment functions with the same monotonic behaviour as the relative increment of decay [1]. We illustrate how relative increment functions may be used to estimate the unknown indefinitely smooth probability density function of unimodal populations.