Odd Generalized Exponential Power Function Distribution: Properties & Applications

Year 2019, Volume: 32 Issue: 1, 351 - 370, 01.03.2019

Amal Hassan , Elsayed Elshrpıeny Rokaya Mohamed

Abstract

In this
article we introduce and study a new four-parameter distribution, called odd
generalized exponential power function distribution based on the odd
generalized exponential generated family. The
proposed model serves as an extension of the two-parameter power distribution
as well as includes the odds exponential power function distribution as a new
sub-model. Expressions for the moments, probability weigthed moments,
quantile function, Bonferroni and Lorenz curves, Rényi entropy and order
statistics are obtained. The model parameters are estimated based on the
maximum likelihood and percentile methods of estimation. A simulation study is
carried out to evaluate and compare the performance of different estimators in
terms of their biases, standard errors and mean square errors. Eventually,
the practical importance and flexibility of the proposed distribution in
modelling real data application is examined.  It has
been concluded that the new distribution works better than some other extensions of the
power function distribution.

Keywords

Power Function distribution, Maximum likelihood estimation, Order statistics

References

• Ahsanullah, M., A characterization of the power function distribution, Communications in Statistics-Theory and Methods, 2(3): 259-262 (1973). Ahsanullah, M., Shakil, M., and Golam Kibria, B. M. G., A characterization of the power function distribution based on lower records, ProbStat Forum 6: 68–72, (2013). Alexander, C., Cordeiro, G. M., Ortega, E. M. M., and Sarabia, J. M., Generalized beta generated distributions. Computational Statistics and Data Analysis, 56: 1880–1897(2012). Ali, M .M., and Woo, J., Inference on reliability P(Y < X) in a power function distribution, Journal of Statistics and Management Science, 8: 681–686, (2005). Ali, M. M., Woo, J. and Yoon, G. E., The UMVUE of mean and right-tail probability in a power function distribution, Estadistica 52: 1–10, 2000 Alzaatreh, A., Lee, C. and Famoye, F., A new method for generating families of continuous distributions, Metron, 71: 63-79 (2013). Balakrishnan, N., and Nevzorov, V., B., A Primer on Statistical Distributions, Wiley, New York, (2003). Bourguignon, M., Silva, R. B., and Cordeiro, G. M, The Weibull–G family of probability distributions, Journal of Data Science, 12: 53–68 (2014). Bursa, N. and Kadilar, G. O, The exponentiated Kumaraswamy power function distribution, Hacettepe University Bulletin of Natural Sciences and Engineering Series Mathematics and Statistics, 46(2): 1 – 19 (2017). Cordeiro, G. M. and Brito, R. S., The beta power distribution, Brazilian Journal of Probability and Statistics, 26: 88-112 (2012). Cordeiro G. M., and de Castro M., A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81: 883-893 (2011). Eugene, N., Lee C., and Famoye, F., Beta-normal distribution and its applications. Communication in Statistics – Theory Methods, 31: 497–512 (2002). Hassan, A. S. and Elgarhy, M., Kumaraswamy Weibull-generated family of distributions with applications, Advances and Applications in Statistics, 48: 205-239 (2016 a). Hassan, A. S. and Elgarhy, M., A new family of exponentiated Weibull-generated distributions, International Journal of Mathematics and its Applications, 4: 135-148 (2016 b). Hassan, A. S., and Hemeda, S. E., The additive Weibull-g family of probability distributions. International Journals of Mathematics and Its Applications, 4: 151-164 (2016). Haq, M. A., Butt, N. S., Usman, R. M., Fattah, A. A. Transmuted power function distribution. Gazi University Journal of Science, 29 (1), 177-185, (2016). Johnson, N. L., Kotz, S. and Balakrishnan, N., Continuous Univariate Distributions, Volume 2, Second edition, Wiley, New York, (1995). Jones, M. C., Families of distributions arising from the distributions of order statistics. Test, 13: 1-43, (2004). Kenney, J. and Keeping, E., Mathematics of Statistics, Volume 1, Third edition, Van Nostrand, Princeton (1962). Kleiber, C., and Kotz, S., Statistical Size Distributions in Economics and Actuarial Sciences Wiley, New York, (2003). Malike, H. G., Exact moments of order statistics from a power-function distribution, Scandinavian Actuaraial Journal, 1-2: 64-69, (1967). Meniconi, M., and Barry, D., The power function distribution: A useful and simple distribution to assess electrical component reliability. Microelectronics Reliability, 36(9): 1207-1212, (1996). Moors, J. J. A., A quantile alternative for kurtosis. Journal of the Royal Statistical Society, Series D (The Statistician), 37(1): 25–32 (1988). Oguntunde, P., Odetunmibi, O. A., Okagbue, H. I. Babatunde, O. S. and Ugwoke, P. O., The Kumaraswamy-power distribution: A generalization of the power distribution, International Journal of Mathematical Analysis, 9(13): 637-645 (2015). Risti´c, M. M., and Balakrishnan, N., The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82: 1191–1206 (2012). Saleem, M., Aslam, M., and Economou, P., On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample, Journal of Applied Statistics 37: 25–40 (2010). Sultan, R., Sultan H., and Ahmad, S. P., Bayesian analysis of power function distribution under double priors. Journal of Statistics Applications and Probability, 3(2): 239-249, (2014). Tahir, M., Alizadehz, M., Mansoor, M., Cordeiro, G. M. and Zubair, M., The Weibull-power function distribution with applications, Hacettepe University Bulletin of Natural Sciences and Engineering Series Mathematics and Statistics, 45(1): 245 – 265 (2016). Tahir, M. H., Cordeiro, G. M., Alizadeh, M., Mansoor, M., Zubair, M. and Hamedani, G. G., The odd generalized exponential family of distributions with applications, Journal of Statistical Distributions and Applications, 2(1): 1-28 (2015). Zaka, A., and Akhter, A. S., 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). Zografos, K., and Balakrishnan, N., On families of beta- and generalized gamma-generated distributions and associated inference, Statistical Methodology, 6: 344–362 (2009).