On the DUS-Kumaraswamy Distribution

Year 2021, Volume: 13 Issue: 1, 29 - 38, 02.01.2021

Kadir Karakaya , İsmail Kınacı , Coşkun Kuş , Yunus Akdoğan

Abstract

Kumaraswamy distribution is introduced by [7] and it is particularly useful for many natural phenomena whose outcomes have lower and upper bounds or bounded outcomes in biomedical and epidemiological research (see [12]). In this paper, a new statistical distribution called DUS-Kumaraswamy is introduced by using DUS transformation (which is recently introduced by [6]) on Kumaraswamy distribution. The proposed distribution has the same domain as Kumaraswamy and it can be used as an alternative model to describe the natural phenomena mentioned above. Several distributional properties such as mean, variance, skewness, kurtosis, Lorenz and Bonferroni curves are studied. The statistical inference on the parameters of Dus-Kumaraswamy is discussed by maximum likelihood methodology. A simulation study is conducted to observe the behaviors of maximum likelihood estimates under different conditions. A numerical example is also presented.

Keywords

Data analysis, Kumaraswamy distribution, Maximum likelihood estimator, Monte Carlo simulation

References

• Bonferroni, C.E. (1930). Elmenti di statistica generale. Libreria Seber, Firenze.
• Canuto, C., Hussaini, A., Quarteroni, A. and Zang, T.A. (2006). Spectral Methods: Fundamentals in Single Domains. Springer-Verlag, New York.
• Cordeiro, G.M. and Santos Brito, R. (2012). The Beta Power Distribution. Brazilian Journal of Probability and Statistics, 26(1), 88-112.
• Deepthi, K.S. and Chacko, V.M. (2020). An Upside-Down Bathtub-Shaped Failure Rate Model Using a DUS Transformation of Lomax Distribution. In Stochastic Models in Reliability Engineering, 81-100. CRC Press.
• Kavya, P. and Manoharan, M. (2020). On a Generalized Lifetime Model Using DUS Transformation. In Applied Probability and Stochastic Processes, 281-291.
• Kumar, D., Singh, U. and Singh, S.K. (2015). A Method of Proposing New Distribution and its Application to Bladder Cancer Patients Data. J. Stat. Appl. Pro. Lett., 2(2), 235-245.
• Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2), 79-88.
• Lagarias, J.C., Reeds, J.A., Wright, M.H. and Wright, P.E. (1998). Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal of Optimization, 9(1), 112-147.
• Lemonte, A.J., Barreto-Souza, W. and Cordeiro, G.M. (2013). The exponentiated Kumaraswamy distribution and its log-transform. Brazilian Journal of Probability and Statistics, 27, 31-53.
• Maurya, S., Kaushik, A. Singh, S. and Singh, U. (2017). A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate. Commun Stat Theory Methods, 46(20), 10359-10372.
• Shaked, M., Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.
• Wang, B.X., Wang, X.K. and Yu, K. (2017). Inference on the Kumaraswamy distribution. Communications in Statistics - Theory and Methods, 46(5), 2079-2090.
• Weibull, W. (1951). A statistical distribution function of wide applicability. J. Appl. Mech. Trans, 18, 293-297.