ALFA GÜÇ BURR-XII DAĞILIMI VE BİR UYGULAMA

Year 2020, Volume: 2 Issue: 1, 33 - 46, 30.06.2020

Selin Tekin , Gamze Özel

Abstract

Bu çalışmada, alfa güç Burr XII (AGBXII) dağılımı önerilerek, dağılımın olasılık yoğunluk fonksiyonu, dağılım fonksiyonu elde edilmiş ve grafikleri çizdirilmiştir. Yaşam, hazard ve kantil fonksiyonları hesaplanmış ayrıca çeyreklik değerleri, medyan, basıklık ve çarpıklık değerleri önemli istatistik özellikleri elde edilmiştir. Daha sonra olabilirlik fonksiyonu ve olabilirlik denklemi elde edilmiş, gerçek veri üzerinden uygulama çalışması yapılmıştır. Parametre değerleri tahmin edilerek, gerçek veriye uyumu test edilmiştir. Hesaplanan uyum iyiliği değerlerine göre veri setine ters Rayleigh (TR) dağılımından daha iyi uyum sağladığı gösterilmiştir.

Keywords

Alfa güç dönüşümü, Burr XII dağılımı, En Çok Olabilirlik Tahmini, Kantil Fonksiyonu

ALFA POWER BURR-XII DISTRIBUTION AND AN APPLICATION

Abstract

In this study, by proposing the distribution of alpha power Burr XII (AGBXII), the probability density function, distribution function are obtained and the graphs are presented. Survival, hazard and quantile functions were derived, and important statistical properties such as quantile, median, kurtosis and skewness values were obtained. Then, the likelihood function and likelihood equation were obtained, and an application study was carried out on real data. Parameter values were estimated and their compliance with the actual data was tested. According to the calculated goodness of fit values, AGBXII has been shown to better match to the data set the inverse Rayleigh (TR) distribution.

Keywords

Alpha power transformation, Burr XII distribution, Maximum likelihood estimation, Quantile function

References

• Mahdavi A. and Kundu, D. (2017), A new method for generating distributions with an application to exponential distribution, Communications in Statistics-Theory and Methods, 46, 13, 6543–6557.
• Abdel Rahman N.S. and El-Bassiouny A.H. (2017), On the alpha-power exponential Weibull distribution, The 2nd National of Mathematics and Its Applications (NCMA17), 1-18.
• Abdel-Ghaly A.A., Al-Dayian G.R. and Al-Kashkari F.H. (1997)., The use of Burr type XII distribution on software reliability growth modeling, Microelectronics and Reliability, 37, 305-313.
• Ahmad Z. (2018), The Zubair-G family of distributions: Properties and applications, Annals of Data Science, 1-14.
• Akdi Y. (2010), Matematiksel İstatistiğe Giriş, Genişletilmiş 2. Baskı, Gazi Kitabevi.
• Burr I.W. (1942), Cumulative frequency functions, Annals of Mathematical Statistics, 13, 215-232.
• Dey S., Ghosh I. and Kumar D. (2018), Alpha-power transformed Lindley distribution: properties and associated inference with application to earthquake data, Annals of Data Science, 1-28.
• Dey S., Nassar M. and Kumar, D. (2019), Alpha power transformed inverse Lindley distribution: A distribution with an upside-down bathtub-shaped hazard function, Journal of Computational and Applied Mathematics, 348, 130-145.
• Efron B. (1988), Logistic regression, survival analysis and the Kaplan-Meier curve, Journal of the American Statistical Association, 83(402), 414-425. Gadde Srinivasa R., Aslam M., Kundu D. (2015), Burr-XII distribution parametric estimation and estimation of reliability of multicomponent stress-strength. Communication in
• Statistics- Theory and Methods, 44, 4953–4961.
• Hassan, A.S., Elgarhy, M., Mohamd, R.E., Alrajhi, S. (2019), On the Alpha power transformed power Lindley distribution, Journal of Probability and Statistics, https://doi.org/10.1155/2019/8024769.
• Moore, D., Papadopoulos, A.S. (2000), The Burr type XII distribution as a failure model under various loss functions, Microelectronics and Reliability, 40, 2117-2122.
• Nasiru S., Mwita P.N. and Ngesa O. (2019), Alpha power transformed Frechet distribution. Applied Mathematics & Information Sciences, 13(1), 129- 141.
• Patrícia F., Paranaíba E.O., Cordeiro G.M. and Pascoa M.A.R. (2013), The Kumaraswamy Burr XII distribution: theory and practice, Journal of Statistical Computation and Simulation, 83(11), 2117-2143.
• Ramadan, D.A., and Magdy W. (2018), On the Alpha-power inverse Weibull distribution. International Journal of Computer Applications, 181, 11, 6-11.
• Ünal C., Cakmakyapan S. and Özel G. (2018), Alpha power inverted exponential distribution: properties and application, Gazi University Journal of Science, 31(3), 954-965.
• Wang F.K. and Keats J.B. (1996), Maximum likelihood estimation of the Burr type XII parameters with censored and uncensored data, Microelectronics and Reliability, 36, 359- 362.
• Wu J.W. and Yu H.Y. (2005), Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan, Applied Mathematics and Computation, 163, 443-482.
• Zimmer W.J., Keats J.B., and Wang F.K. (1998), The Burr XII distribution in reliability analysis, Journal of Quality Technology, 30, 386-394.