Katlanmış üstel güç dağılımının parametrelerinin tahmini için karşılaştırmalı bir çalışma

Abstract

Katlanmış dağılımlar, ölçümlerin cebirsel işaretlerinin önemli olmadığı veri setleri için yaygın olarak kullanılırlar. Bu nedenle, mühendislik, finans, ekonomi v.b. bir çok alanda kapsamlı uygulamaları vardır. Modelleme esnekliği ve kolay kullanımı olan katlanmış üstel güç (FEP) dağılımı yeni önerilmiştir [1]. Bu çalışmada bu nedenle, FEP dağılımının bilinmeyen parametrelerinin farklı parametrik yöntemlerle tahmin edilmesi ele alınmıştır. En çok olabilirlik (ML), sıradan ve ağırlıklandırılmış en küçük karerler (LS ve WLS), Cramer von Mises (CVM) ve aralıkların çarpımının maksimumu (MPS) metotları tahmin sürecinde kullanılmıştır. Ele alınan tahmin edicilerin performansı, Monte-Carlo simülasyon çalışmasında yan ve hata kareler ortalaması (MSE) kriterleri kullanılarak karşılaştırılmıştır. Sonuçlar, MPS yönteminin rakiplerinden daha iyi bir performansa sahip olduğunu göstermiştir. Literatürden alınan iki gerçek hayat uygulaması ele alınmıştır. 

Keywords

• Etkinlik,Katlanmış üstel güç dağılımı,Tahmin,Yan

A Comparative study for estimation of the parameters of the folded exponential power Ddstribution

Abstract

Folded distributions are commonly used for the data set which is obtained without regarding the algebraic signs of the measurements. Therefore, they have extensive applications in different fields, such as engineering, finance, insurance and so on. Folded exponential power (FEP) distribution is a newly proposed distribution which has modeling flexibility and easy usage [1]. In this study, we therefore consider different parametric methods for estimating the unknown parameters of FEP distribution. Maximum likelihood (ML), ordinary and weighted least squares (LS and WLS), Cramer von Mises (CVM) and maximum product of spacings (MPS) methods are used during the estimation process. The performances of the considered estimators are compared in a Monte-Carlo simulation study via bias and mean squared error (MSE) criteria. Results show that MPS method outperforms its rivals. Two real life applications taken from the literature are also considered. 

Keywords

• Bias,Efficiency,Estimation,Folded exponential power distribution

References

1. S. Nadarajah, S.A.A. Bakar, 2015, New folded models for the log-transformed Norwegian fire claim data, Communications in Statistics-Theory and Methods, 44(20), 4408-4440.
2. V. Brazauskas, A. Kleefeld, 2011, Folded and log-folded-t distributions as models for insurance loss data, Scandinavian Actuarial Journal, 2011(1), 59-74.
3. M. Chen, F. Kianifard, 2003, Estimation of treatment difference and standard deviation with blinded data in clinical trials, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 45(2), 135-142.
4. S. Jung, M. Foskey, J. S. Marron, 2011, Principal arc analysis on direct product manifolds, The Annals of Applied Statistics, 5(1), 578-603.
5. F. C. Leone, L. S. Nelson, R. B. Nottingham, 1961, The folded normal distribution, Technometrics, 3, 543-550.
6. M. Y. Liao, 2010, Economic tolerance design for folded normal data, International Journal of Production Research, 48(14), 4123-4137.
7. S. Psarakis, J. Panaretoes, 1990, The folded t distribution, Communications in Statistics-Theory and Methods, 19, 2717-2734.
8. K. Cooray, S. Gunasekera, M. M. A. Ananda, 2006, The folded logistic distribution, Communications in Statistics-Theory and Methods, 35, 385-393.

9. M. T. Subbotin, 1923, On the law of frequency of errors, Matematicheskii Sbornik, 31, 296-301.
10. K. Cooray, 2010, Generalized Gumbel distribution, Journal of Applied Statistics, 37, 171-179.
11. W. Gui, 2013, Statistical inferences and applications of the half exponential power distribution, Journal of Quality and Reliability Engineering, Article ID 219473, 9 pages.
12. F. G. Akgul, 2018, Comparison of the estimation methods for the parameters of exponentiated reduced kies distribution, Süleyman Demirel University Journal of Natural and Applied Sciences, 22(3), 1209-1216.
13. Y. M. Kantar, B. Senoglu, 2008, A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter, Computers & Geosciences, 34(12), 1900-1909.
14. F. Louzada, P. L. Ramos, G. S. Perdona, 2016, Different estimation procedures for the parameters of the extended exponential geometric distribution for medical data, Computational and mathematical methods in medicine, Article ID 8727951, 12 pages.
15. J .J. Swain, S. Venkatraman, J. R. Wilson, 1988, Least-squares estimation of distribution functions in Johnson’s translation system, Journal of Statistical Computation and Simulation, 29(4), 271-297.
16. R. C. H. Cheng, N. A. K. Amin, 1983, Estimating parameters in continuous univariate distributions with a shifted origin, Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394-403.
17. B. Ranneby, 1984, The maximum spacing method. An estimation method related to the maximum likelihood method, Scandinavian Journal of Statistics, 11(2), 93-112.
18. Statisticat, LLC., 2018, LaplacesDemon: Complete Environment for Bayesian Inference. Bayesian-Inference.com. R package version 16.1.1. https://web.archive.org/web/20150206004624/http://www.bayesian-inference.com/software.