The Generalized Odd Lomax Generated Family of Distributions with Applications

Year 2019, Volume: 32 Issue: 2, 737 - 755, 01.06.2019

Waleed Marzouk , Farrukh Jamal A-hadi N. Ahmed A.a. E Ahmed

Abstract

Through this article, a new generated family of distributions under the
name of "The generalized odd Lomax-G family" by adding three
additional parameters to generalize any continuous baseline distribution is
provided. For the generalized odd Lomax-G family main properties, stochastic
orderings, entropy measures have been studied. Three special models have been
discussed for the new family. By using the maximum likelihood method, The model
parameters are estimated. Simulation is carried out for one of the sub-models
to check the asymptotic behavior of the maximum likelihood estimates. We
explained the efficiency of the new family by using four applications to the
real world.

Keywords

Lomax, Lifetime data, Maximum likelihood estimation, Order statistics

References

• 1. Abdul-Moniem, I. B. and Abdel-Hameed, H. F., "On exponentiated Lomax distribution", International Journal of Mathematical Archive, 3(5): 2144-2150, (2012).2. Alzaatreh, A., Lee, C., &Famoye, F., "A new method for generating families of continuous distributions", Metron, 71(1): 63-79,(2013).3. Bidram, H., Alamatsaz, M. H., &Nekoukhou, V., "On an extension of the exponentiated Weibull distribution", Communications in Statistics-Simulation and Computation, 44(6): 1389-1404, (2015).4. Cordeiro, G. M., &Nadarajah, S., "Closed-form expressions for moments of a class of beta generalized distributions", Brazilian journal of probability and statistics, 25(1): 14-33, (2011).5. Cordeiro, G. M., Ortega, E. M., Popović, B. V., &Pescim, R. R., "The Lomax generator of distributions: Properties, minification process and regression model", Applied Mathematics and Computation, 247: 465-486, (2014). 6. Ghitany, M. E., Al-Hussaini, E. K., & Al-Jarallah, R. A., "Marshall–Olkin extended Weibull distribution and its application to censored data", Journal of Applied Statistics, 32(10): 1025-1034, (2005).7. Gupta, R. C., & Gupta, R. D., "Proportional reversed hazard rate model and its applications", Journal of Statistical Planning and Inference, 137(11): 3525-3536, (2007).8. Gupta, R. C., Gupta, P. L., & Gupta, R. D., "Modeling failure time data by Lehman alternatives", Communications in Statistics-Theory and methods, 27(4): 887-904, (1998).9. Gupta, R. D., &Kundu, D., "Theory & methods: Generalized exponential distributions", Australian & New Zealand Journal of Statistics, 41(2): 173-188, (1999).10. Kotz, S., Lumelskii, Y., &Pensky, M., The Stress-Strength Model and its Generalizations: Theory and Applications, World Scientic, New Jersey, (2003).11. Kundu, D., &Raqab, M. Z., "Generalized Rayleigh distribution: different methods of estimations", Computational statistics & data analysis, 49(1): 187-200, (2005).12. Lee, C.,Famoye, F., &Alzaatreh, A. Y., "Methods for generating families of univariate continuous distributions in the recent decades", Wiley Interdisciplinary Reviews: Computational Statistics, 5(3): 219-238, (2013).13. Lomax, K. S., "Business failures: Another example of the analysis of failure data", Journal of the American Statistical Association, 49(268): 847-852, (1954).14. Mandouh, R. M., "Lomax-Modified Weibull Distribution: A New Generalization", Journal of Advances in Mathematics and Computer Science, 27(1): 1-7; Article no. JAMCS.38975, (2018). 15. Marshall, A. W., &Olkin, I., "A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families", Biometrika, 84(3): 641-652, (1997).16. Mead, M. E. A., "A new generalization of Burr XII distribution", Journal of Statistics: Advances in Theory and Applications 12(2):53–73, (2014).17. Mudholkar, G. S., & Srivastava, D. K., "Exponentiated Weibull family for analyzing bathtub failure-rate data", IEEE transactions on reliability, 42(2): 299-302, (1993).18. Raqab, M. Z., Madi, M. T., &Kundu, D., "Estimation of P (Y< X) for the three-parameter generalized exponential distribution", Communications in Statistics-Theory and Methods, 37(18): 2854-2864, (2008).19. Rayleigh, L., "XII. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase", The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 10(60): 73-78, (1880).20. Smith, R. L., & Naylor, J. C., "A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution", Applied Statistics, 358-369, (1987).21. Tahir, M. H., Cordeiro, G. M., Mansoor, M., & Zubair, M., "The Weibull-Lomax distribution: properties and applications", Hacettepe Journal of Mathematics and Statistics, 44(2): 461-480, (2015).22. Vidondo, B., Prairie, Y. T., Blanco, J. M., & Duarte, C. M., "Some aspects of the analysis of size spectra in aquatic ecology", Limnology and Oceanography, 42(1): 184-192, (1997).23. Weibull, W., "A Statistical Distribution Function of Wide Applicability", Journal of applied mechanics, 103(730): 293-297, (1951).