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

Yıl 2018, Cilt 14, Sayı 29, 151 - 168, 19.07.2019

Öz

Hayat tabloları, nüfus istatistikleri esas alınarak düzenlenir ve yaşlara göre ölüm hızlarını, ölüm olasılıklarını, yıllara göre hayatta kalanların sayıları ve yaşanması beklenen süreleri ihtiva eder. Bu tablolar sosyal güvenlik kurumları, sigorta şirketleri, emeklilik kurumları vs. tarafından aktüeryal hesaplamalarda kullanılır. Türkiye’de de bu tablolar TÜİK tarafından yayınlanmaktadır. En son 2013-2016 yıllarını kapsayan tablolar yayınlanmıştır. Bu çalışmamızda tablolardaki yüz yıllık sürede hayatta kalanlar istatistiklerinin doğrusal-olmayan fonksiyonlarla temsiliyetini istatistiksel analiz ile araştırdık. Amacımıza uygun olarak Gompertz büyüme fonksiyonunu kullandık ve tablolardaki toplam nüfus ve kadın ve erkek nüfus için üç hesaplama yaptık. Başarılı istatistiki sonuçlar aldık. Haytta kalanlar için % 9-11 arası küçülme hızları tespit ettik. Aynı verilere Richards lojistik büyüme fonksiyonunu uyguladığımızda iyi sonuçlar alamadık. Elimizdeki serilere dayanarak düzenlediğimiz yıllara göre artan ölümler serilerine Richards fonksiyonunu uyguladığımızda uygun ve başarılı sonuçlar aldık. % 20-23 arası büyüme oranları bulduk. Her iki fonksiyon analizinde de önceliğimiz doğrusal olmayan fonksiyonların ve fonksiyonların hesaplanmasında kullanılan istatistiksel yöntemlerin hesap ve ispat gücünü ve faydasını ortaya koymak, teorik bilgileri verilerle buluşturmaktı. Başardığımız kanısındayım. 

Kaynakça

  • llen, R. G. D., Mathematical Analysis for Economists, Macmillan and Co. Ltd., 1969. Bacaër, N., A Short History of Mathematical Population Dynamics, Springer-Verlag London Limited, 2011 Gompertz, Benjamin, On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies, Philosophical Transactions of the Royal Society of London, Vol. 115. (1825), pp. 513-583. İskender, C., Türkiye Nüfus Büyümesi ve Tahminleri: Matematiksel Büyüme Modelleri ve İstatistiksel Analiz ile Kuramsal ve Uygulamalı bir Yaklaşım, Ekonometri ve İstatistik e-Dergisi 14 (2018), 75-141, http://dergipark.gov.tr/iuekois/issue/39224/461853 King, G., Life Contingencies Part II (Including Life Annuites and Assurances), Institute of Actuaries Text Book of the Principles of Interest, Life Annuities, and Assurances, and Their Practical Application, second edition, Charles&Edwin Layton, 1902, London. Edelstein-Keshet L.,Integral Calculus: Mathematics 103, University of British Columbia, 2010. Pearl, R., The Biology of Death, Monographs on Experimental Biology, Philadelphia and London, J.B. Lippincott Company, 1920 Pearl, Raymond and Reed, J. Lowell, (1920) On the Rate of Growth of the Population of the United States Since 1790 and Its Mathematical Representation, Procedings of the National Academy of Sciences, Volume 6 June 15, Number 6. Richards, F. J. (1959). A Flexible Growth Function for Empirical Use, Journal of Experimental Botany, 10, 290–300. Russell, L. H., A First Course in Differential Equations for Scientists and Engineers, R. L. Herman- Version date: August 17,2018. SAS Institute Inc. 2008. SAS/STAT® 9.2 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. 2013. SAS/STAT® 13.1 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. 2017. SAS/STAT® 14.3 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. SAS/STAT. (2009). SAS/STAT® 9.2 user’s guide the NLIN procedure (Book Excerpt) (2nd electronic book). Winsor, P. Charles, (1932) The Gompertz Curve as a Growth Curve , Proceedings of the National Academy of Sciences of the United States of America, Vol. 18, No. 1 (Jan. 15, 1932), pp. 1-8.

Application of Non-linear Growth Functions for Turkish 2014-2016 Life Tables

Yıl 2018, Cilt 14, Sayı 29, 151 - 168, 19.07.2019

Öz

In this study, a representation of survivors statistics from TÜİK 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. 

Kaynakça

  • llen, R. G. D., Mathematical Analysis for Economists, Macmillan and Co. Ltd., 1969. Bacaër, N., A Short History of Mathematical Population Dynamics, Springer-Verlag London Limited, 2011 Gompertz, Benjamin, On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies, Philosophical Transactions of the Royal Society of London, Vol. 115. (1825), pp. 513-583. İskender, C., Türkiye Nüfus Büyümesi ve Tahminleri: Matematiksel Büyüme Modelleri ve İstatistiksel Analiz ile Kuramsal ve Uygulamalı bir Yaklaşım, Ekonometri ve İstatistik e-Dergisi 14 (2018), 75-141, http://dergipark.gov.tr/iuekois/issue/39224/461853 King, G., Life Contingencies Part II (Including Life Annuites and Assurances), Institute of Actuaries Text Book of the Principles of Interest, Life Annuities, and Assurances, and Their Practical Application, second edition, Charles&Edwin Layton, 1902, London. Edelstein-Keshet L.,Integral Calculus: Mathematics 103, University of British Columbia, 2010. Pearl, R., The Biology of Death, Monographs on Experimental Biology, Philadelphia and London, J.B. Lippincott Company, 1920 Pearl, Raymond and Reed, J. Lowell, (1920) On the Rate of Growth of the Population of the United States Since 1790 and Its Mathematical Representation, Procedings of the National Academy of Sciences, Volume 6 June 15, Number 6. Richards, F. J. (1959). A Flexible Growth Function for Empirical Use, Journal of Experimental Botany, 10, 290–300. Russell, L. H., A First Course in Differential Equations for Scientists and Engineers, R. L. Herman- Version date: August 17,2018. SAS Institute Inc. 2008. SAS/STAT® 9.2 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. 2013. SAS/STAT® 13.1 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. 2017. SAS/STAT® 14.3 User’s Guide. Cary, NC: SAS Institute Inc. SAS Institute Inc. SAS/STAT. (2009). SAS/STAT® 9.2 user’s guide the NLIN procedure (Book Excerpt) (2nd electronic book). Winsor, P. Charles, (1932) The Gompertz Curve as a Growth Curve , Proceedings of the National Academy of Sciences of the United States of America, Vol. 18, No. 1 (Jan. 15, 1932), pp. 1-8.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Cemil İSKENDER> (Sorumlu Yazar)
Ekonomist
0000-0003-2841-5964
Türkiye

Yayımlanma Tarihi 19 Temmuz 2019
Başvuru Tarihi 1 Kasım 2018
Kabul Tarihi 15 Ocak 2019
Yayınlandığı Sayı Yıl 2018, Cilt 14, Sayı 29

Kaynak Göster

APA İskender, C. (2019). Türkiye 2014-2016 Hayat Tablolarında Doğrusal-olmayan Büyüme Fonksiyonları Uygulaması . Ekoist: Journal of Econometrics and Statistics , 14 (29) , 151-168 . Retrieved from https://dergipark.org.tr/tr/pub/ekoist/issue/47194/594196