Üstel Model Uygulamaları ile Genelleştirilmiş Dağılımların Yeni Bir Kumaraswamy Sınıfı

Öz

Bu yazıda, alfa gücü Kumaraswamy (AK) sınıfı olarak adlandırılan yeni bir genelleştirilmiş dağılım sınıfı türetilmiştir, AK sınıfı tarafından üç önemli dağılım sınıfı iç içe yerleştirilmiştir. Bazı matematiksel özellikler incelenir ve maksimum olabilirlik (MLE) kullanılarak bir parametre tahmin yöntemi elde edilir. Alfa gücünün tahmin edici davranışını incelemek için önyükleme yaklaşımı kullanan bir simülasyon çalışması yapılmıştır. (AKE) dağıtımı. AKE dağılımının esnekliğini göstermek için gerçek bir veri seti araştırılır.

Anahtar Kelimeler

• Alfa gücü Kumarasamy dağılımı
• anlar
• sıra istatistikleri
• maksimum olabilirlik tahmini
• önyükleme yaklaşımı.

A New Kumaraswamy Class of Generalized Distributions with Applications to Exponential Model.

Öz

In this paper, a new class of generalized distributions, so-called the alpha power Kumaraswamy (AK) class, is derived, three important classes of distributions are nested by the AK class. Some mathematical properties are studied and a parameters estimation method using maximum likelihood (MLE) is obtained. A simulation study using bootstrapping approach is performed to study the estimators behavior of the alpha power Kumaraswamyexponential (AKE) distribution. A real data set is investigated to illustrate the flexibility of the AKE distribution.

Anahtar Kelimeler

• The alpha power Kumarasamy distribution
• moments
• order statistics
• maximum likelihood estimation
• bootstrapping approach

Kaynakça

1. [1] Mahdavi, A. & Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Method, 46, 6543-6557.
2. [2] Ahmed, M.A. (2020). On the alpha power Kumaraswamy distribution: Properties, simulation and application. Revista Colombiana de Estadística, 43, 285-313.
3. [3] Wahed, A.S. (2006). A general method of constructing extended families of distributions from an existing continuous class. Journal of Probability and Statistical Science, 4, 165-177.
4. [4] Kumaraswamy, P. (1980). A generalized probability density function for double- bounded random-processes. Journal of Hydrology, 46, 79-88.
5. [5] Cordeiro, G.M., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation & Simulation, 81, 883-898.
6. [6] Pescim, R.R., Cordeiro, G.M., Demétrio, C.G., Ortega, E.M. & Nadarajah, S. (2012). The new class of Kummer beta generalized distributions. SORT-Statistics and Operations Research Transactions, 153-180.
7. [7] McDonald, J.B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52, 647-664.
8. [8] Alexander, C, Cordeiro, G.M., Ortega, E.M.M. & Sarabia J.M. (2012). Generalized beta-generated distributions. Comput Stat Data Anal., 56, 1880-1897.

9. [9] El-Sherpieny, E.A. & Ahmed, M.A. (2014). On the kumaraswamy Kumaraswamy distribution. International Journal of Basic and Applied Sciences, 3, 372-381.
10. [10] Mahmoud, M.R., El-Sherpieny, E.A. & Ahmed, M.A. (2015). The new Kumaraswamy Kumaraswamy family of generalized distributions with application. Pakistan Journal of Statistics and Operations Research, 11, 159-180.
11. [11] Meniconi, M. & Barry, D. (1996). The power function distribution: A useful and simple distribution to assess electrical component reliability. Microelectronics Reliability, 36, 1207-1212.
12. [12] Johnson, N.L., Kotz, S. & Balakrishnan, N. (1995). Continuous Univariate Distributions. John wiley and Sons, New York .
13. [13] Greenwood, J.A., Landwehr, J.M., Matalas, N.C. & Wallis, J.R. (1979). Probability weighted moments definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15, 1049-1054.
14. [14] Gradshteyn, I.S. & Ryzhik, I.M. (2000). Tables of Integrals, Series and Products.Academic Press, San Diego, CA.
15. [15] Ali Ahmed, M. (2021). The new form Libby-Novick distribution. Communications in Statistics-Theory and Methods, 50, 540-559.‏
16. [16] Meeker, W.Q. & Escobar, L.A. (1998). Statistical Methods for Reliability Data. John Wiley, New York.
17. [17] Arnold, B.C., Balakrishnan, N. & Nagaraja, H.N. (1992). A First Course in Order Statistics. John Wiley and Sons, Inc., New York.
18. [18] Garthwait, P.H., Jolliffe, I.P. & jones, B. (2002). Statistical Inference. Prentice HallInternational (UK) Limited, London.
19. [19] Pearson, K. (1895). Contributions to the mathematical theory of evolution. II. Skew variations in homogeneous material. Philosophical Transactions of the Royal Society of London, Series A, 186, 343-414.
20. [20] Merovcia, F. & Puka, L. (2014). Transmuted Pareto distribution. Prob Stat Forum, 7, 1-111.