DOĞUM ORANININ MODELLENMESİ İÇİN İSTATİSTİKSEL DAĞILIMLARIN KARŞILAŞTIRILMASI

Abstract

Nüfus istatistikleri ve demografi, ülkenin yaşam kalitesini, sosyal ve sağlık durumunu, nüfusun durumunu, nüfus yapısındaki değişimi ve bunun ekonomik hayata etkisini gösteren önemli göstergelerdir. Demografide, bir nüfusun büyümesini ölçmek için kaba doğum hızı kullanılmaktadır. Bu çalışmada, Türkiye'deki istatistiki bölge sınıflandırmasına göre kaba doğum hızı değerlerinin istatistiki dağılımlara uyumu araştırılmaktadır. Elde edilen sonuçlar karşılaştırıldığında, Türkiye'de kaba doğum hızı değerlerini modellemek için Normal, Log-Normal, Exponential, Gamma ve Weibull dağılımlarına göre en iyi uyumu Gumbel dağılımı sağlamaktadır. Karşılaştırılan dağılımlar arasında, Gumbel dağılımının log olabilirlik (logL), Akaike bilgi kriterleri (AIC) ve Bayes bilgi kriterleri (BIC) değerleri tüm modeller arasında en düşük olduğundan, CBR verilerini en iyi sunan model Gumbel modelidir. Ayrıca, karşılaştırılan dağılımlar ile sonuçlar grafiklerle desteklenmiştir.

Keywords

• Kaba doğum hızı
• uç değer dağılımları
• Gumbel dağılımı
• Nüfus tahminleri
• Türkiye nüfusu

A COMPARISON OF STATISTICAL DISTRIBUTIONS FOR THE CRUDE BIRTH RATE DATA

Abstract

Population statistics and demographic are important indicators to show the country's quality of life, social and health, the status of the population, the change in the population structure, and its effect on economic life. In demography, the crude birth rate is used to measure the growth of a population. In this study, we perform the crude birth rate values by statistical regions in Türkiye with some statistical distributions. When the results are compared, the Gumbel distribution provides the best fit to model the crude birth rate values than Normal, Log-Normal, Exponential, Gamma, and Weibull distributions. Among compared distributions, the Gumbel model is the best model to present the CBR data since log likelihood (logL), Akaike information criteria (AIC) and Bayesian information criteria (BIC) values of the Gumbel distribution are the lowest among all models. In addition, the results with the compared distributions are supported by graphs.

Keywords

• Crude birth rate
• Extreme value distributions
• Gumbel distribution
• Population estimates
• Turkish population

References

1. Abd Ellatif, S.M.A.E. (2017). A comparative study to estimate and forecasting mortality using demographic and statistical models [Ph.D. thesis]. Sudan University of Technolegy & Sciences, Sudan.
2. Almalki, S.J. & Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety, 124, 32-55.
3. Anderson, R.M. (2014). The population dynamics of infectious diseases: Theory and applications. Springer, New York.
4. Basak, I. & Balakrishnan, N. (2012). Estimation for the three-parameter gamma distribution based on progressively censored data. Statistical Methodology, 9(3), 305-319.
5. Brauer, F. & Castillo-Chavez, C. (2013). Mathematical models in population biology and epidemiology. Texts in applied mathematics. Springer, New York.
6. Brown, G.W. & Flood, M.M. (1947). Tumbler mortality. Journal of the American Statistical Association. 42(240), 562-574.
7. Demirci Biçer, H. & Atakan, C. (2012). Gamma, Weibull ve Log-Normal dağılımlarının doğru seçim olasılıklarına göre ayrıştırılması. İstatistik Araştırma Dergisi, 9(1), 11-20.
8. Gómez, Y. M., Bolfarine, H. & Gómez, H. W. (2019). Gumbel distribution with heavy tails and applications to environmental data. Mathematics and Computers in Simulation, 157, 115-129.

9. Hamilton, B.E., Martin, J.A. & Ventura, S.J. (2009). Births: Preliminary data for 2007. National Vital Statistics Reports, 57(12), 1-23. Hannon, B., Ruth, M. & Levin, S.A. (1997). Modeling dynamics biological systems. Modeling Dynamic Systems. Springer, New York.
10. Hirose, H. (1995). Maximum likelihood parameter estimation in the three-parameter gamma distribution. Computational Statistics & Data Analysis, 20(4), 343-354.
11. Jafari, A.A. & Abdollahnezhad, K. (2017). Testing The equality means of several log-normal distributions. Communications in Statistics - Simulation and Computation, 46(3), 2311-2320.
12. Lee, E.T. & Wang, J. (2003). Statistical methods for survival data analysis, 476. John Wiley & Sons, Inc.
13. Marrec, L., Bank, C. & Bertrand, T. (2022). Solving the stochastic dynamics of population growth. BioRxiv. 1-15.
14. Oseni, B.A. & Ayoola, F.J. (2013). Fitting the Statistical Distribution for Daily Rainfall in Ibadan, Based On Chi-Square and Kolmogorov-Smirnov Goodness-Of-Fit Tests. West African Journal of Industrial and Academic Research, 7(1), 93-100.
15. Spoorenberg, T. (2015). Evaluation and analysis of fertility data. Regional Workshop on the Production of Population Estimates and Demographic Indicators. Addis Ababa. United Nations, Department of Economic and Social Affairs.
16. The World Bank, (2022). Retrieved July 21, 2023 from https://data.worldbank.org/indicator/SP.DYN.CBRT.IN?end=2020&locations=EU&most_recent_value_desc=true&start=2020.
17. Tsoularis, A. & Wallace, J. (2002). Analysis of logistic growth models. Mathematical Biosciences, 179, 21– 55.
18. TurkStat, Birth Statistics (2022a). Retrieved July 21, 2023 from https://data.tuik.gov.tr/Bulten/Index?p=Birth-Statistics-2022-49673&dil=2#:~:text=Crude%20birth%20rate%20was%2012.2,12.2%20per%20thousand%20in%202022.
19. TurkStat, (2022b). Retrieved July 21, 2023 from https://data.tuik.gov.tr/Bulten/Index?p=Birth-Statistics-2020-37229&dil=2.
20. Vaidyanathan, V. & Lakshmi, R.V. (2015). Parameter Estimation in Multivariate Gamma Distribution. Statistics, Optimization Information Computing, 3(2), 147-159.
21. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 9(1951), 293-297.
22. Yonar, A. & Yapıcı Pehlivan, N. (2022). Evaluation and comparison of metaheuristic methods to estimate the parameters of gamma distribution. Nicel Bilimler Dergisi, 4(2), 96-119.