Sağkalım ve Güvenilirlik Analizlerinde Yeni Bir Olasılık Dağılımı

Yıl 2021, , 651 - 659, 30.12.2021

Selen Çakmakyapan , Gamze Özel

https://doi.org/10.7240/jeps.938953

Öz

Sağkalım ve güvenilirlik analizleri; bir makinenin, malzemenin ya da bir canlının “ömrünü sürdürme ihtimali” ve “bu ömrün sonlanmasına kadar geçen süre” ile ilgilenilir. Bu analizlerde, verinin en iyi şekilde temsil edilebilmesi için veriyi modelleyecek olasılık dağılımının brlirlenmesi çok önemlidir. Bu çalışmada, bu alanda kullanılabilecek yeni bir olasılık dağılımı tanımlanmış ve bu dağılıma ilişkin istatistiksel özellikler elde edilmiştir. Uygulama iki farklı, gerçek güvenilirlik veri seti üzerinde gerçekleştirilmiş ve bu verileri modellemede daha önce kullanılmış olasılık dağılımları ile karşılaştırılmıştır. Önerilen dağılımın veriyi diğer dağılımlardan çok daha iyi modellediği gösterilmiştir.

Anahtar Kelimeler

lindley dağılımı, lomax dağılımı, tahmin, modelleme

Kaynakça

• [1] A. N. Marshall, and I. Olkin, A New method for adding a parameter to a family of distributions with applications to the exponential and Weibull families”, Biometrika vol. 84, pp. 641-552, 1997.
• [2] N. Eugene, C. Lee, and F,. Famoye, Beta-normal distribution and its applications, Communications in Statistics: Theory and Methods ,vol. 31, pp. 497-512, 2002.
• [3] K. Zografos, K. and N. Balakrishnan, On families of beta- and generalized gamma-generated distributions and associated inference, Statistical Methodology, vol. 6, pp. 344-362, 2009.
• [4] A. Alzaghal, F. Famoye, and C. Lee, Exponentiated T-X family of distributions with some applications, International Journal of Probability and Statistics vol. 2, pp. 31–49, 2013.
• [5] G. M. Cordeiro, and M. de Castro, A new family of generalized distributions, Journal of Statistical Computation and Simulation vol. 81, pp. 883-893, 2011.
• [6] A. Alzaatreh, C. Lee, and F. Famoye, A new method for generating families of distributions, Metron vol. 71, pp. 63-79, 2013.
• [7] A. S. Hassan, and S. E. Hemeda, The additive Weibull-g family of probability distributions, International Journals of Mathematics and Its Applications, vol. 4, pp. 151-164, 2016.
• [8] S Cakmakyapan,. and G. Ozel, The Lindley Family of Distributions: Properties and Applications, vol. 46, no.1, pp. 1113-1137, 2016.
• [9] F. Gomes-Silva, A. Percontini, E. de Brito, M. W. Ramos , R. Venancio, and G. Cordeiro, The Odd Lindley-G Family of Distributions, Austrian Journal of Statistics, vol. 46, pp. 65-87, 2017.
• [10] M. Mead, G. Cordeiro, A. Afify, H. Al-Mofleh, The Alpha Power Transformation Family: Properties and Applications. Pakistan Journal of Statistics and Operation Research. vol. 15. pp. 525-545, 2019. 10.18187/pjsor.v15i3.2969.
• [11] H. Reyad, M. C. Korkmaz, A.Z., Afify, G. G. Hamedani, and S. Othman, The Frechet Topp Leone-G family of distributions: Properties, characterizations and applications. Annals of Data Science, 2019. https://doi.org/10.1007/s40745-019-00212-9.
• [12] D. V. Lindley Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society Series B vol. 20, pp. 102-107, 1958.
• [13] J. Mazucheliand and J. A: Achcar, The Lindley distribution applied to competing risks lifetime data, Computer Methods and Programs in Biomedicine vol. 104, pp. 188-92, 2011.
• [14] M. Chahkandi, and M. Ganjali, On some lifetime distributions with decrasing failure rate, Computational Statistics and Data Analysis vol. 53, pp. 4433–4440, 2009.
• [15] M.C. Bryson, Heavy-tailed distribution: properties and tests, Technometrics vol. 16, pp. 161–68, 1974.
• [16] P.R. Tadikamalla, A look at the Burr and realted distributions, International Statistical Review vol. 48, pp. 337–344, 1980.
• [17] S.D. Durbey, Compound gamma, beta and F distributions, Metrika vol. 16, pp. 27–31, 1970.
• [18] A.B. Atkinson, and A.J. Harrison, Distribution of Personal Wealth in Britain Cambridge University Press, Cambridge, 1978.
• [19] C.M. Harris, The Pareto distribution as a queue service descipline, Operations Research vol. 16, pp. 307–313, 1968.
• [20] A. Corbellini, L. Crosato, P. Ganugi, and M. Mazzoli, Fitting Pareto II distributions on firm size: Statistical methodology and economic puzzles. Paper presented at the International Conference on Applied Stochastic Models and Data Analysis, Chania, Crete, 2007.
• [21] O. Holland, A. Golaup, and A. H. Aghvami, Traffic characteristics of aggregated module downloads for mobile terminal reconfiguration, IEEE proceedings on Communications vol. 135, pp. 683–690, 2006.
• [22] A. S. Hassan, and A. S Al-Ghamdi. Optimum step stress accelerated life testing for Lomax distribution, Journal of Applied Sciences Research vol. 5, 2153-2164, 2009.
• [23] I. S Gradshteyn, and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 2007.
• [24] E.T. Lee, and J.W. Wang, Statistical Methods for Survival Data Analysis, 3rd ed., Wiley, New York, 2003.
• [25] A.J. Lemonte, and G.M. Cordeiro, An extended Lomax distribution, Statistics, 2011.
• [26] R.S. Chhikara, and J.L. Folks The inverse Gaussian distribution as a lifetime model. Technometrics vol. 19, pp. 461-468, 1977.
• [27] S Shrestha, and K. V. Kumar, Bayesian Analysis of Extended Lomax Distribution, International Journal of Mathematics Trends and Technology vol. 7 no. 1, 2014.