TRANSMUTED POWER FUNCTION DISTRIBUTION

Abstract

This study provides a three parameter Transmuted Power Function distribution that is the generalization of the Power Function distribution. Structural properties of the proposed distribution was derived including survival, hazard rate, moments, quintiles, mode, Rényi entropy, smallest and largest densities of ordered statistics. Maximum likelihood method is used for estimating the model parameters. Two real data sets are used to compare the flexibility of the new model versus the other distributions

Keywords

• Transmuted,Power Function,Reliability Function,Moment Generating Function,Rényi Entropy,Order Statistics,Maximum Likelihood Estimation

References

1. Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
2. Abdul-Sathar, E., Renjini, K., Rajesh, G., & Jeevanand, E. (2015). Bayes estimation of Lorenz curve and Gini-index for power function distribution. South African Statistical Journal, 49(1), 21-33.
3. Afify, A. Z., Nofal, Z. M., Yousof, H. M., El Gebaly, Y. M., & Butt, N. S. (2015). The Transmuted Weibull Lomax Distribution: Properties and Application. Pakistan Journal of Statistics and Operation Research, 11(1), 135-152.
4. Ahsanullah, M. (1973). A characterization of the power function distribution. Communications in Statistics-Theory and Methods, 2(3), 259-262.
5. Ahsanullah, M., & Kabir, A. L. (1974). A characterization of the power function distribution. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, 95-98.
6. Al-Zahrani, B., & Sagor, H. (2014). The poisson-lomax distribution. Revista Colombiana de Estadística, 37, 225-245.
7. Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications & Probability, 2(1), 11-20.
8. Balakrishnan, N., & Nevzorov, V. B. (2004). A primer on statistical distributions: John Wiley & Sons.

9. Cordeiro, G. M., & dos Santos Brito, R. (2012). The beta power distribution. Brazilian journal of probability and statistics, 26(1), 88-112.
10. Cordeiro, G. M., Ortega, E. M., & da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.
11. Dallas, A. (1976). Characterizing the Pareto and power distributions. Annals of the Institute of Statistical Mathematics, 28(1), 491-497.
12. Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions: John Wiley & Sons.
13. Gui, W., Zhang, S., & Lu, X. (2014). The Lindley-Poisson distribution in lifetime analysis and its properties. Hacettepe Journal of Mathematics and Statistics, 43(6), 1063-1077.
14. Hassan A. S., Abd-Elfattah, A.M. and Mokhtar A. H (2015). The Complementary Burr III Poisson Distribution. Australian Journal of Basic and Applied Sciences. 9(11), 219-228.
15. Haq, M. A., Usman, R. M., & Fateh, A. A. (2015). A Study on Kumaraswamy Power Function Distribution. Submitted.
16. Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994).
17. Continuous univariate distributions, vol. 1-2: New York: John Wiley & Sons.
18. Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences (Vol. 470): John Wiley & Sons.
19. Meniconi, M., & Barry, D. (1996). The power function distribution: A useful and simple distribution to assess electrical component reliability. Microelectronics Reliability, 36(9), 1207-1212.
20. Merovci, F. (2013a). Transmuted lindley distribution. International Journal of Open Problems in Computer Science & Mathematics, 6.
21. Merovci, F. (2013b). Transmuted rayleigh distribution. Austrian Journal of Statistics, 42(1), 21-31.
22. Murthy, D., Xie, M., & Jiang, R. (2004). Weibull models (Vol. 505): John Wiley and Sons.
23. Naveed-Shahzad, M., Asghar, Z., Shehzad, F., & Shahzadi, M. (2015). Parameter Estimation of Power Function Distribution with TL-moments. Revista Colombiana de Estadística, 38(2), 321-334.
24. Oguntunde, P., Odetunmibi, O., Okagbue, H., Babatunde, O., & Ugwoke, P. (2015). The Kumaraswamy-Power Distribution: A Generalization of the Power Distribution. International Journal of Mathematical Analysis, 9(13), 637-645.
25. Ramos, M. W. A., Percontini, A., Cordeiro, G. M., & da Silva, R. V. (2015). The Burr XII Negative Binomial Distribution with Applications to Lifetime Data. International Journal of Statistics and Probability, 4(1), p109.
26. Shaw, W. T., & Buckley, I. R. (2007). The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions. Submitted, Feb, 7, 64.
27. Sinha, S. K., Singh, P., Singh, D., & Singh, R. (2008). Preliminary test estimators for the scale parameter of power function distribution. Journal of Reliability and Statistical Studies, 1(1), 18-24.
28. Smith, R. L., & Naylor, J. (1987). A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 358-369.
29. Sultan, R., Sultan, H., & Ahmad, S. (2014). Bayesian Analysis of Power Function Distribution under Double Priors. Journal of Statistics Applications and Probability, 3(2), 239-249.
30. Tahir, M., Alizadeh, M., Mansoor, M., Cordeiro, G. M., & Zubair, M. (2014). The weibull-power function distribution with applications. Hacettepe university bulletin of natural sciences and engineering series b: mathematics and statistics. doi: DOI: 10.15672/HJMS.2014428212
31. Zaka, A., & Akhter, A. S. (2014a). Bayesian Analysis of Power Function Distribution Using Different Loss Functions. International Journal of Hybrid Information Technology, 7(6), 229-244.
32. Zaka, A., & Akhter, A. S. (2014b). 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.
33. Zaka, A., Feroze, N., & Akhter, A. S. (2013). A note on Modified Estimators for the Parameters of the Power Function Distribution. International Journal of Advanced Science and Technology, 59, 71-84.