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Abstract

The Kumaraswamy distribution is an important probability distribution used to model several hydrological problems as well as various natural phenomena whose process values are bounded on both sides. In this paper, we introduce a new family of inverse Kumaraswamy distribution and then explore its statistical properties. Conventional maximum likelihood estimators are considered for the parameters of this distribution and estimation based on dual generalized order statistics is outlined. A particular sub-model of this family; namely, the inverse Kumaraswamy- Weibull distribution is considered and some of its statistical properties are obtained. Estimation efficiency is numerically evaluated via a simulation study and two real-data applications of the proposed distribution are provided as well.

Keywords

Inverse Kumaraswamy distribution Weibull distribution Maximum Likelihood Estimation Dual Generalized Order Statistics Least-Square Estimation

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How to Cite
Daghistani, A. M., Al-Zahrani, B., & Shahbaz, M. Q. (2023). A New Inverse Kumaraswamy Family of Distributions: Properties and Application. Pakistan Journal of Statistics and Operation Research, 19(2), 313-326. https://doi.org/10.18187/pjsor.v19i2.4295
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References

  1. Afify, A., Marzouk, W., Al-Mofleh, H., Ebraheim, H., and Abdel-Fatah, N. (2022). The Extended Failure Rate Family: Properties and Applications in the Engineering and Insurance Fields. Pak. J. Stat., 38:165–196.
  2. Akaike, H. (1998). Information Theory and an Extension of the Maximum Likelihood Principle. In Springer Series in Statistics, pages 199–213. Springer New York.
  3. Al-Fattah, A. M., El-Helbawy, A. A., and Al-Dayian, G. R. (2017). Inverted Kumaraswamy Distribution: Properties and Estimation. Pak. J. Stat., 33(1), 37–61.
  4. Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71, 63–79.
  5. Cordeiro, G., Ortega, E., and Nadarajah, S. (2010). The Kumaraswamy Weibull distribution with application to failure data. J. Franklin Institute., 347:1399–1429.
  6. Cordeiro, G. M. and Castro, M. d. (2011). A New Family of Generalized Distributions. J. Stat. Comp. Simul., 81:883–898.
  7. Cox, D. R. and Oakes, D. (2018). Analysis of Survival Data, Chapman and Hall., New York.
  8. Daghistani, A. M., Al-Zahrani, B., and Shahbaz, M. Q. (2019). Relations for Moments of Dual Generalized Order Statistics for a New Inverse Kumaraswamy Distribution. Pak. J. Stat. and Oper. Res.,15(4):989–997.
  9. Fletcher, S. G. and Ponnambalam, K. (1996). Estimation of reservoir yield and storage distribution using moments analysis. J. of Hydrology, 182, 259–275.
  10. Ganji, A., Ponnambalam, K., Khalili, D., and Karamouz, M. (2006). Grain yield reliability analysis with crop water demand uncertainty. Stoch. Envi. Res. And Risk Assess., 20, 259–277.
  11. Gradshteyn, I. and Ryzhik, I. (2007). Table of Integrals, Series and Products, volume 20, Elsevier.
  12. Grebenc, A. (2011). A new continuous entropy function and its inverse. Facta Uni. Physics, Chemistry and Technology, 9, 65–70.
  13. Kamps, U., Cramer, E., and Burkschat, M. (2003). Dual Generalized Order Statistics. Metron, 61, 13–26.
  14. Khan, M. S., King, R., and Hudson, I. (2016). Transmuted Kumaraswamy Distribution. Stat. Trans., 17, 183–210.
  15. Koutsoyiannis, D. and Xanthopoulos, T. (1989). On the parametric approach to unit hydrograph identification. Water Res. Manag., 3, 107–128.
  16. Kumaraswamy, P. (1980). A Generalized Probability Density Function for Double-Bounded Random Processes. J. of Hydrology, 46, 79–88.
  17. Nassar, M. and Nada, N. K. (2011). The beta generalized Pareto distribution. J. of Stat.: Adv. Theo. Appl., 6.
  18. Ponnambalam, K., Seifi, A., and Vlach, J. (2001). Probabilistic design of systems with general distributions of parameters. Int. J. Circuit Theo. Appl., 29, 527–536.
  19. Schwarz, G. (1978). Estimating the Dimension of a Model. Ann. of Stat., 6, 461–464.
  20. Seifi, A., Ponnambalam, K., and Vlach, J. (2000). Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values. Ann. Opera. Res., 99, 373–383.
  21. Shahbaz, M. Q., Ahsanullah, M., Shahbaz, S. H., and Al-Zahrani, B. M. (2016). Ordered Random Variables: Theory and Applications. Springer-Verlag, New York.
  22. Sundar, V. and Subbiah, K. (1989). Application of double bounded probability density function for analysis of ocean waves. Ocean Engine., 16, 193–200.
  23. Widemann, B. T. (2011). Kumaraswamy and beta distribution are related by the logistic map. arXiv, Stat. Theo.