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In this article, we dened a new four-parameter model called Marshall-Olkin extended power Lomax distribution and studied its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for real data.
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- Alzaatreh, A., Lee, C., and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71:63–79, doi:10.1007/s40300–013–0007–y.
- Andrews, D. and Herzberg, A. (1985). Data: A Collection of Problems from Many Fields for the Student and Research Worker. Springer-Verlag, New York, doi:10.1007/978-1-4612-5098-2.
- Arnold, B., Balakrishnan, N., and Nagaraja, H. (1992). First Course in Order Statistics. Society for Industrial and Applied Mathematics, New York, John Wiley, doi:10.1137/1.9780898719062.
- Barlow, R., Toland, R., and Freeman, T. (1984). A Bayesian Analysis of Stress Rupture Life of Kevlar 49/epoxy Spherecal Pressure Vessels. Proc. Conference on Applications of Statistics.
- Cordeiro, G., Ortega, E., and Cunha, D. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11:887–904, doi:10.1080/03610929808832134.
- Eugene, N., Lee, C., and Famoye, F. (2002). Beta- normal distribution and its applications. Communications in Statistics - Theory and Methods, 31:497–512, doi:10.1081/STA–120003130.
- Gupta, R., Ghitany, M., and Al-Mutairi, D. (2010). Estimation of reliability from marshallolkin extended lomax distribution. Journal of Statistical Computation and Simulation, 80:937–947, doi:10.1080/00949650902845672.
- Gupta, R., Gupta, P., and Gupta, R. (1998). Modeling failure time data by lehman alternatives. Communications in Statistics -Theory and Methods, 27:887–904, doi:10.1080/03610929808832134.
- Kotz, S., Lumelskii, Y., and Pensky, M. (2003). The Stress-Strength Model and Its Generalizations Theory and Applications. World Scientiﬁc Corporation, Singapore, doi:10.1142/5015.
- Lemonte, A., Barreto-Souza, W., and Cordeiro, G. (2013). The exponentiated kumaraswamy distribution and its log-transform. Brazilian Journal of Probability and Statistics, 27:31–53, Retrieved from http://www.jstor.org/stable/43601233.
- Lomax, K. (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association, 49:847–852, doi: 10.1080/01621459.1954.10501239.
- Marshall, A. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrica, 84:641–652, Retrieved from http://www.jstor.org/stable/2337585.
- Rady, E. A., Hassanein, W. A., and Elhaddad, T. A. (2016). The power lomax distributionwith an application to bladder cancer data. SpringerPlus, 5:1–22, doi:10.1186/s40064–016–3464–y.
- Risti´c, M. and Nadarajah, S. (2013). A new lifetime distribution. journal of statistical computation and simulation. Journal of Statistical Computation and Simulation, 84:135–150, doi:10.1080/00949655.2012.697163.
- Torabi, H. and Montazeri, N. (2012). The gamma-uniform distribution and its applications. Kybernetika, 48:16–30.