The exponentiated Kumaraswamy-power function distribution

Year 2017, Volume: 46 Issue: 2, 277 - 292, 01.04.2017

Nurbanu Bursa Gamze Ozel

Abstract

In this paper, the exponentiated Kumaraswamy-power function distribution is introduced. Some structural properties of the proposed distribution including the shapes of the density, hazard and quantile functions are explored. Besides, skewness and kurtosis measures are investigated. The method of maximum likelihood is used for estimating model parameters. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared with some well-known distributions. Then, an application is presented with a real data set to illustrate the usefulness of the proposed distribution.

Keywords

Kumaraswamy-power function distribution, maximum likelihood estimation, hazard function

References

• Zaka, A. and Akhtar, A.S. Estimation of parameters of the Power function distribution: Different classical methods, Pakistan Journal of Statistics and Operation Research, 9 (2), 213-224, 2013.
• Haq, M.A.u., Butt, N.S., Usman, R.M. and Fattah, A.A. Trunsmuted power function dis- tribution, Gazi University Journal of Science, 29 (1),177-185, 2016.
• Meniconi, M. and Barry, D. The power function distribution: A useful and simple distribu- tion to assess electrical component reliability, Microelectronics Reliability, 36 (9), 1207-1212, 1996.
• Ahsanullah, M. and Kabir, A. A characterization of the power function distribution, The Canadian Journal of Statistics/La Revue Canadianne de Statistique, 2 (1), 95-98, 1974.
• Zaka, A. and Akhter, A. Modified moment, maximum likelihood and percentile estimators for the parameters of the power function distribution, Pakistan Journal of Statistics and Operation Research, 10 (4), 369-388, 2014.
• Zaka, A. and Akhter, A. Bayesian analysis of power function distribution using different loss functions, International Journal of Hybrid Information Technology, 7 (6), 229-244, 2014.
• Zaka, A., Froze, N. and Akhter, A. A note on modified estimators for the parameters of the power function distribution, International Journal of Advanced Science and Technology, 59 ,71-84, 2013.
• Sultan, R., Sultan, H. and Ahmad, S. Bayesian analysis of power function distribution under double priors, Journal of Statistics Applications and Probability, 3 (2), 239-249, 2014.
• Sinha, S.K., Singh, P. and Singh, D.C. Preliminary test estimators for the scale parameter of power function distribution, Journal of Reliability and Statistical Studies, 11 (1), 18-24, 2008.
• Abdulsathar, E.I., Jeevanand, E.S. and Nair, K.R.M. Bayes estimation of Lorenz curve and Gini-index for power function distribution, South African Statistical Journal, 49 (1), 21-33, 2015.
• Cordeiro, G. and dos Santos Brito, R. The beta power distribution, Brazilian Journal of Probability and Statistics, 26 (1), 88-112, 2012.
• Oguntunde, P., Odetunmibi, O., Okagbue, H., Babatunde, O. and Ugwoke, P. The Kumaraswamy-power distribution: A generalization of the power distribution, International Journal of Mathematical Analysis, 9 (13), 637-645, 2015.
• Tahir, M., Alizadeh, M., Mansoor, M., Cordeiro, G. and Zubair, M. The Weibull-power function distribution with applications, Hacettepe Journal of Mathematics and Statistics, 45 (1), 245-265, 2016.
• Shakeel, M., Haq , M., Hussain, I., Abdulhamid, A. and Faisal, M. Comparison of two new robust parameter estimaton methods for the power function distribution, Plos One, 8, 1-11, 2016.
• Mansoor, M., Tahir, M., Alzaatreh, A., Corediro, G., Zubair, M. and Ghazali, S. An extended Fret distribution: Properties and applications, Journal of Data Science, 14, 167-188, 2016.