Lomax-Weibull Distribution with Properties and Applications in Lifetime Analysis
Keywords:
Competing risk approach, Lomax distribution, Weibull distribution, Lomax Weibull distribution, Moments, Entropy, Maximum likelihood estimation
Abstract
The paper introduces a new distribution called the Lomax-Weibull distribution using the competing risk approach of constructing lifetime distributions. Some structural and mathematical properties of the proposed lifetime distribution are considered. Parameter estimation of the Lomax Weibull distribution is obtained using maximum likelihood estimation. The applicability and flexibility of the new distribution in lifetime analysis is illustrated with the aid of two real life examples.
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International Journal of Mathematical Archive , vol.3, pp.2144-2150.
[2] Al-Zahrani, B. and Sagor, H. (2014). The Poisson-Lomax distribution.de Estadística , vol.37, pp.225-245.Revista Colombiana
[3] Ali, M.M., Korkmaz, M. Ç., Yousof, H.M. and Butt, N.S. (2019). Odd Lindley-Lomax model: Statistical properties and applications. Pakistan Journal of Statistics and Operations
Research , vol.15, pp.419-430.
[4] Alzaghal, A. and Hamed, D. (2019). New families of generalized Lomax distribution:
Properties and Applications. International Journal of Statistics and Probability , vol.8, pp.51-
68.
[5] Ashour, S.K. and Eltehiwy, M.A. (2013). Transmuted Lomax distribution. American Journal
of Applied Mathematics and Statistics , vol.1, pp.121-127.
[6] Cordeiro, G.M. and de Castro, M. (2011). A new family of generalized distributions. Journal
of Statistical Computation and Simulation , vol.81, pp.883-898.
[7] Cordeiro, G.M., Ortega, E.M.M. and Popovi¢, B.V.Lomax distribution. Journal of Statistical Computation and The Simulation gamma iFirst , doi:10.1080/00949655.2013.822869. (2013).
[8] Fatima, K., Jan, U. and Ahmad, S.P. (2018). Statistical properties of Rayleigh Lomax
distribution with applications in survival analysis. Journal of Data Science , vol.16, pp.531-
548.
[9] Ghitany, M.E., AL-Awadhi, F.A. and Alkhalfan, L.A. (2007). Marshall-Olkin extended
Lomax distribution and its applications to censored data. Communications in Statistics-
Theory and Methods , vol.36, pp.1855-1866
[10] Lemonte, A.J. and Cordeiro, G.M. (2013). An extended Lomax distribution.
Journal of Statistics , vol.47, pp.800-816.
[11] Lomax, K.S. (1954). Business failures: Another example of the analysis of failure data.
Journal of the American Statistical Association , vol.49, pp.847-852.
[12] Murthy, D.N.P., Xie, M. and Jiang, R. (2004). Weibull Models. Hoboken, New Jersey, USA.
John Wiley and Sons Inc.
[13] Nicholas, M.D. and Padgett, W.J. (2006). A bootstrap control chart for Weibull percentiles.
Quality and Rrliability Engineering International , vol.22, pp.141-151.
[14] Oguntunde, P.E., Khaleel, M.A., Ahmed, M.T., Adejumo, A.O. and Odetunmibi,O.A.
(2017). A new generalization of the Lomax distribution with increasing, decreasing and
constant failure rate. Modelling and Simulation in Engineering , vol.2017, pp.1-6.
[15] Oluyede, B.O., Foya, S., Warahena-Liyanage, G. and Huang, S. (2016). The log-logistic
Weibull distribution with applications to lifetime data. Austrian Journal of Statistics , vol.45,
pp.43-69.
[16] Pham, H. and Lai, C.D. (2007). On recent generalizations of the Weibull distributions. IEEE
Transactions on Reliability , vol.56, pp.454-458.
[17] Rady, E.A., Hassanein, W.A. and Elhaddad, T.A. (2016). The power Lomax distribution
with an application to bladder cancer data. SpringerPlus , vol.5:1838.
[18] Rajab, M., Aleem, M., Nawaz, T. and Daniyal, M. (2013). On ?ve parameter beta Lomax
distribution. Journal of Statistics , vol.20, pp.102-118.
[19] Sarhan, A. M. and Zaindin, M. (2009). Modi?ed Weibull distribution.
Journal of Applied Science , vol.11, pp.123-136.
[20] Tahir, M.H., Cordeiro, G.M., Mansoor, M. and Zubair, M. (2014). The Weibull-Lomax
distribution: Properties and Apllications. Hacettepe Journal of Mathematics and Statistics ,
vol.44, pp.461-480.
[21] Tahir, M.H., Hussain, M.A., Cordeiro, G.M., Hamedani, G.G., Mansoor, M. and Zubair, M.
(2016). The Gumbel-Lomax distribution: Properties and Apllications. Journal of Statistical
Theory and Applications , vol.15, pp.61-79.
[22] Weibull, W. (1939). A Statistical Theory of the Strength of Materials. Ingeniors
Vetenskapa Academiens Handligar, Stockholm , vol.151, pp.197?203.
[23] Weibull, W. (1951). A Statistical Distribution Function with Wide Applicability.
Journal of Applied Mechanics , vol.18, pp.293-297.
[24] Xie, M. and Lai, C.D. (1996). Reliability analysis using an additive Weibull model with
bathtub-shaped failure rate function. Reliability Engineering System Safety , vol.52, pp.87-93.
Published
2020-07-19
How to Cite
Osagie, S. A., & Osemwenkhae, J. E. (2020). Lomax-Weibull Distribution with Properties and Applications in Lifetime Analysis. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2020(1), 718 - 732. Retrieved from http://ijmso.unilag.edu.ng/article/view/969
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