Türkiye 2014-2016 Hayat Tablolarında Doğrusal-olmayan Büyüme Fonksiyonları Uygulaması

Abstract

In this study, a representation of survivors statistics from TUIK Turkish mortality tables (2014-2016) with non-linear growth functions was investigated by applying advanced statistical methods. Firstly, the Gompertz function was used for this purpose. Gompertz function was specifially developed by Benjamin Gompertz for the analysis of mortality tables. We calculated three functions for both male and female populations and for total population. Successful statistical results were obtained for all groups. Intrinsic contraction rates ranging from 9 to 11% were calculated for the survivors of the three series. Although we have been successful with statistical tests of Gompertz function, Richards logistic growth function didn’t give us satisfactory statistical results when applied this function to survivors series of Turkish mortality table. This was not a suprise because we knew that logistic growth function was already developed by Verhulst mainly for mathematical explanation of increasing population figures not for decreasing population figures . Turkish mortality tables does not include number of dying population by ages. Then we recalculated number of dying population by years from the survivors figures of Turkish mortality tabels. In this case Richards logistic function gave successful statistical results with the number of dying population by years. The intrinsic growth rate was found between 20 and 23% for total population and male and female populations. As result we used Gompertz function successfully for survivors population of mortality table which is a decreasing serie by years and Richards logistic function for number of dying population which is an increasing serie by years. Our priority in the analysis of both functions was to show the calculation and proof power of non-linear growth functions and advanced statistical methods were applied for this reason. Six successful functions were obtained of which three were for the survivors series using the Gompertz function and three were for the number of dying population series using the Richards logistic growth curve.