The novel kumaraswamy extended garima distribution, statistical properties and its application

Abstract

This essay aims to present a novel Kumaraswamy Extended Garima distribution family. We obtain a cumulative distribution function, the failure rate, the risk rate, the inverse risk function, the odd function, the cumulative risk function, the moment r-th, the characteristic function of the moment generating function, the moments, the mean and the variance, Lorenz and Bonferroni curves, order statistics, MLE, mean time between failures (MTBF), Renyi and Tsallis entropies. The MLE technique estimates the parameters of the new Kumaraswamy Extended Garima distribution. The parameters of the MLE technique are derived using a nonlinear system of equations and the Symmetric Information Matrix. Furthermore, the consequences are analogous to others because they are probability distributions. According to the findings, the proposed distribution fits these data sets better than existing probability distributions.

Keywords

• Garima distribution
• Kumaraswamy distribution
• Cumulative distribution function
• Characteristic function
• Symmetric information matrix.

Yeni Kumaraswamy genişletilmiş Garima dağılımı istatistiksel özellikleri ve uygulaması

Abstract

Bu makale yeni bir Kumaraswamy Genişletilmiş Garima dağıLım ailesini sunmayı amaçlamaktadır. Kümülatif bir dağılım fonksiyonu, başarısızlık oranı, risk oranı, ters risk fonksiyonu, tek fonksiyon, kümülatif risk fonksiyonu, moment r-th, moment üreten fonksiyonun karakteristik fonksiyonu, momentler, ortalama ve varyans, Lorenz ve Bonferroni eğrileri, sıra istatistikleri, MLE, arızalar arasındaki ortalama süre (MTBF), Renyi ve Tsallis entropileri gibi özellikleri elde ettik. MLE tekniği, yeni Kumaraswamy Extended Garima dağılımının parametrelerini tahmin eder. MLE tekniğinin parametreleri, doğrusal olmayan bir denklem sistemi ve Simetrik Bilgi Matrisi kullanılarak türetilir. Ayrıca sonuçlar olasılık dağılımları olduğundan diğerlerine benzer. Bulgulara göre, bu veri setlerine önerilen dağılım, mevcut olasılık dağılımlarından daha iyi uymaktadır.

Keywords

• Garima dağılımı
• Kumaraswamy dağılımı
• Kümülatif dağılım fonksiyonu
• Karakteristik fonksiyon
• Simetrik bilgi matrisi.

References

1. [1] Almanjahie I. M., Dar J. G., Laksaci, A., Ahmad, I., A new probability model for modeling of strength of carbon fiber data: properties and applications, Environmental and Ecological Statistics. 28(3), 523-547, (2021).
2. [2] Asiribo O.E., Mabur T.M., Soyinka A.T., On the Lomax-Kumaraswamy distribution, Benin Journal of Statistics, Vol, 2, 107-120, (2019).
3. [3] Bader M.G., Priest A.M., Statistical aspects of fibre and bundle strength in hybrid composites. Progress in science and engineering of composites, 1129-1136, (1982).
4. [4] Bjerkedal T., Acquisition of Resistance in Guinea Pies infected with Different Doses of Virulent Tubercle Bacilli, American Journal of Hygiene, 72(1), 130-48, (1960).
5. [5] Carrasco J.M., Ferrari, S.L., Cordeiro G.M., A new generalized Kumaraswamy distribution. arXiv preprint arXiv:1004.0911, (2010).
6. [6] Carrasco J.M., Cordeiro G.M., An extension of the Kumaraswamy distribution, International Journal of Statistics and Probability, 6(3), 61, (2017).
7. [7] Cordeiro G.M., de Castro M. A new family of generalized distributions, Journal of statistical computation and simulation, 81(7), 883-898, (2011).
8. [8] Dey S., Mazucheli J., Nadarajah S., Kumaraswamy distribution: different methods of estimation, Computational and Applied Mathematics, 37, 2094-2111, (2018).

9. [9] Eghwerido J.T., Ogbo J.O., Omotoye A. E., The Marshall-Olkin Gompertz distribution: properties and applications. Statistica, 81(2), 183-215, (2021).
10. [10] El-Sherpieny E.S.A., Ahmed M.A., On the kumaraswamy Kumaraswamy distribution, International Journal of Basic and Applied Sciences, 3(4), 372, (2014).
11. [11] Garg M., On Distribution of Order Statistics from Kumaraswamy Distribution, Kyungpook mathematical journal, 48(3), (2008).
12. [12] Gomes A.E., da-Silva C.Q., Cordeiro G.M., Ortega E.M., A new lifetime model: the Kumaraswamy generalized Rayleigh distribution, Journal of statistical computation and simulation, 84(2), 290-309, (2014).
13. [13] Iqbal Z., Tahir M.M., Riaz N., Ali S.A., Ahmad M., Generalized inverted kumaraswamy distribution: properties and application, Open Journal of Statistics, 7(4), 645-662, (2017).
14. [14] Jones M.C.,Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages, Statistical methodology, 6(1), 70-81, (2009).
15. [15] Kumaraswamy P.A., Generalized probability density function for double-bounded random processes, Journal of hydrology, 46(1-2), 79-88, (1980).
16. [16] Linhart H., Zucchini W., Model Selection, Wiley. New York, (1986).
17. [17] Mead M.E., Afify A.Z., Hamedani G.G., Ghosh I., The beta exponential Fréchet distribution with applications, Austrian Journal of Statistics, 46(1), 41-63, (2017).
18. [18] Mitnik P.A., Baek S., The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation, Statistical Papers, 54, 177-192, (2013).
19. [19] Mitnik P.A., New properties of the Kumaraswamy distribution, Communications in Statistics-Theory and Methods, 42(5), 741-755, (2013).
20. [20] Mohiuddin M., Rather A.A., Subramanian C., Dar S.A., Transmuted Garima Distribution: Properties and Applications, Journal of Xidian University, 14(3), (2020).
21. [21] Nadarajah S., On the distribution of Kumaraswamy, Journal of Hydrology, 348(3), 568-569, (2008).
22. [22] Nichols M.D., Padgett W.J., A bootstrap control chart for Weibull percentiles, Quality and reliability engineering international, 22(2), 141-151, (2006).
23. [23] Paranaiba P.F., Ortega E.M., Cordeiro G.M., Pascoa M.A D., The Kumaraswamy Burr XII distribution: theory and practice, Journal of Statistical Computation and Simulation, 83(11), 2117-2143, (2013).
24. [24] Rather A.A., Subramanian C., A New Exponentiated Distribution with Engineering Science Applications, J. Stat. Appl., Pro, 9, 127-137, (2020).
25. [25] Salman M.S., Comparing Different Estimators of two Parameters Kumaraswamy Distribution, Journal of Babylon University, Pure and Applied Sciences, 25(2), 395-402, (2017).
26. [26] Tahir M.H., Zubair M., Mansoor M., Cordeiro G.M., Alizahdehk M., Hamedani G., A new Weibull-G family of distributions, Hacettepe Journal of Mathematics and statistics, 45(2), 629-647, (2016).
27. [27] Tahir M.H., Hussain M.A., Cordeiro G.M., El-Morshedy M., Eliwa M.S., A new Kumaraswamy generalized family of distributions with properties, applications, and bivariate extension, Mathematics, 8(11), 1989, (2020).
28. [28] Team R.C., R: A language and environment for statistical computing computer program, version 3.6. 1. R Core Team, Vienna, Austria (2019).
29. [28] Team R.D.C., R: A language and environment for statistical computing, (2010).
30. [29] Yang T., Statistical properties of Kumaraswamy generalized inverse Weibull distribution, (2012).
31. [30] Wang B.X., Wang X.K., Yu K., Inference on the Kumaraswamy distribution, Communications in Statistics-Theory and Methods, 46(5), 2079-2090, (2017).