TY - JOUR T1 - Sıralı Küme Örneklemesi ile Kumaraswamy Dağılımı Parametrelerinin Tahmin Edilmesinde Genetik Algoritma Kullanılması TT - On Estimating Parameters of the Kumaraswamy Distribution with Ranked Set Sampling Using Genetic Algorithms AU - Kılıç, Adil AU - Arslan, Güvenç PY - 2019 DA - August DO - 10.19113/sdufenbed.471565 JF - Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi JO - J. Nat. Appl. Sci. PB - Süleyman Demirel Üniversitesi WT - DergiPark SN - 1308-6529 SP - 367 EP - 373 VL - 23 IS - 2 LA - tr AB - Bu çalışmada, Kumaraswamy dağılımının parametrelerininen çok olabilirlik yöntemi ile tahmin edilmesi genetik algoritma yaklaşımıkullanılarak araştırılmıştır. Ayrıca basit rasgele örneklemeye göre daha iyisonuç verebileceği düşünülerek parametrelerin tahmin edilmesinde sıralı kümeörneklemesi de incelenmiştir. Genetik algoritma yaklaşımı, Kumaraswamy dağılımıparametrelerinin pozitif olma koşulunun hesaba katılması nedeniyle tercihedilmiştir. Ek olarak genetik algoritma yaklaşımında en çok olabilirlikfonksiyonunun türev bilgisine ihtiyaç duyulmaması da hesaplamalarda kolaylıksağlamaktadır. Genetik algoritma kullanılarak elde edilen her iki örneklemeyöntemine ait olabilirlik tahmin edicilerinin performanslarınınkarşılaştırılması için yan, hata kareler ortalaması ve etkinliklerihesaplanmıştır. Simülasyon çalışmasındaki hesaplamalar için R yazılımı veilgili paketler kullanılmıştır. KW - Kumaraswamy dağılımı KW - Sıralı küme örneklemesi KW - En çok olabilirlik tahmini KW - Genetik algoritma N2 - In thispaper, genetic algorithm approach is used to estimate parameters of theKumaraswamy distribution with maximum likelihood method. In addition ranked setsampling is used since it is expected to give better results in comparison tosimple random sampling. Genetic algorithm approach is chosen because it isrelatively more convenient in terms of satisfying positivity constraints forthe parameters of the Kumaraswamy distribution. Also there is no need to use derivativesin the genetic algorithm approach. Bias, MSE and efficiency is calculated tocompare performaces of maximum likelihood estimators for ranked set samplingand simple random sampling obtained by using genetic algorithms. The R softwareand related packages are preferred for calculations in the simulation study. CR - [1] Kumaraswamy, P. 1980. A generalized Probability Density Function for Double-Bounded Random Processes. Journal of Hydrology, 46(1980), 79-88. CR - [2] Jones, M. C. 2009. Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6(2009), 70-81. CR - [3] Hussian, M. A. 2014. Bayesian and Maximum Likelihood Estimation for Kumaraswamy Distribution based on Ranked Set Sampling. American Journal of Mathematics and Statistics, 4(2014), 30-37. CR - [4] McIntyre, G. A. 1952. A Method for Unbiased Selective Sampling, using Ranked Sets. Australian Journal of Agricultural Research, 1952 385-390. CR - [5] Patil, G. P., Surucu, B. and Egemen D. 2002. Ranked set sampling. Wiley StatsRef: Statistics Reference Online, 2002. CR - [6] Takahasi, K., and Wakimoto, K. 1968. On unbiased estimates of the population mean based on the sample stratifed by means of ordering. Annals of the Institute of Statistical Mathematics, 1968, 1-31. CR - [7] Dell, T. R., and Clutter, J. L. 1972. Ranked set sampling theory with order statistics background. Biometrics, 1972, 545-555. CR - [8] Stokes, S. L. 1977. Ranked Set Sampling with Concomitant Variables. Communications in Statistics-Theory and Methods, 1977, 1207-1211. CR - [9] Samawi, H. M. 1996. Stratified Ranked Set Sample. Pakistan Journal of Statıstıcs-All Serıes, 12(1996), 9-16. CR - [10] Samawi, H. M., Ahmed, M. S., and Abu-Dayyeh, W. 1996. Estimating the Population Mean using Extreme Ranked Set Sampling. Biometrical Journal, 38(1996), 577-586. CR - [11] Al-Saleh, M. F., and Al-Kadiri M. A. 2000. Double-Ranked Set Sampling. Statistics & Probability Letters, 48(2000), 205-212. CR - [12] Al- Saleh, M. F., and Al-Omari A. I. 2002. Multistage Ranked Set Sampling. Journal of Statistical planning and Inference, 102(2002), 273-286. CR - [13] Muttlak, H. A. 2003. Investigating the Use of Quartile Ranked Set Samples for Estimating the Population Mean. Applied Mathematics and Computation, 146(2003), 437-443. CR - [14] Holland, J.H. 1975. Adaptation in Natural and Artifcial Systems. MIT Press. CR - [15] Goldberg, D. 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley. CR - [16] Chong, E. KP., Zak, S. H. 2013. An Introduction to Optimization. 2nd, John Wiley & Sons. CR - [17] R Core Team (2017). R: A language and environment for statistical computing., R Foundation for Statistical Computing, Vienna, Austria., [Çevrimiçi]. Available: https://www.R-project.org/. CR - [18] C. D. Marie Laure Delignette-Muller, fitdistrplus: An R Package for Fitting Distributions, Journal of Statistical Software 64(4), 1-34, 2015. [Çevrimiçi]. Available: http://www.jstatsoft.org/v64/i04/. CR - [19] R. V. John C. Nash, Unifying Optimization Algorithms to Aid Software System Users: optimx for R, Journal of Statistical Software, 43(9), 1-14, 2011. [Çevrimiçi]. Available: http://www.jstatsoft.org/v43/i09/. CR - [20] Scrucca, L., GA: A Package for Genetic Algorithms in R., Journal of Statistical Software, 53(4), 1-37., 2013. [Çevrimiçi]. Available: http://www.jstatsoft.org/v53/i04/. CR - [21] Yee, T. W., The VGAM Package for Categorical Data Analysis., Journal of Statistical Software, 32(10), 1-34., 2010. [Çevrimiçi]. Available: http://www.jstatsoft.org/v32/i10/. UR - https://doi.org/10.19113/sdufenbed.471565 L1 - https://dergipark.org.tr/tr/download/article-file/782109 ER -