the Exponential Modified Weibull Logistic Distribution (EMWL)

  • Manal Mohamed Nassar
  • Salwa Said Radwan
  • Ayat Salah Elmasry
Keywords: Modified Weibull distribution, Quantile function, maximum likelihood estimation


This paper introduces a new distribution named Exponential Modified Weibull logistic distribution. This distribution generalizes the following distributions: (1) Linear Failure Rate Logistic Distribution, (2) Weibull Logistic Distribution, (3) Rayleigh Logistic Distribution, (4) Exponential Logistic Distribution, where the failure rate, Weibull, Rayleigh and exponential distributions are the distributions most used for analyzing lifetime data. The properties of the new distribution are derived that include expressions for the r^thmoment, characteristic function and quantile function. The estimation of model parameters are performed by the method of maximum likelihood and hence evaluation of the performance of maximum likelihood estimation using simulation.

Author Biographies

Manal Mohamed Nassar
Professor, Department of Mathematical Statistics& Mathematics,Faculty of Science.
Salwa Said Radwan
Assistant Professor, Department of Mathematical Statistics& Mathematics, Faculty of Science (girls Branch)
Ayat Salah Elmasry
Assistant Lecturer, Department of Mathematical Statistics& Mathematics, Faculty of Science.


Aarset, M.V. (1987), “How to identify bathtub hazard rate”, IEEE Transactions on Reliability, 36(1), 106-108.

AlKadim, K.A. and Boshi, M.A. (2013), “Exponential Pareto Distribution”, Mathematical Theory and Modeling, 3, 135-146.

Bassiouny, A.H. Abdo, N.F. and Shahen, H.S. (2015), “Exponential Lomax Distribution”, In-ternational Journal of Computer Applications, 13, 24-29.
Bebbington, M., Lai, C. D. and Zitikis, R. (2007),” A flexible Weibull extension”, Reliability Engineering and System Safety, 92, 719-726.

Jiang, H., Xie, M. and Tang, L. C. (2010), “ On MLEs of the parameters of a modified Weibull distribution for progressively type-2 censored samples”, Journal of Applied Statistics, 37(4), 617-627.

Lai, C. D., Xie, M. and Murthy, D. N. P. (2003), “ A modified Weibull distribution”, IEEE Transactions on Reliability, 52(1), 33-37.

Miller, Jr., R.G. (1981), Survival Analysis, John Wiley, New York.
Sarhan, A.M. and Zaindin, M. (2009), “ Modified Weibull distribution”, Applied Sciences, 11, 123-136.
Shannon,C.E. (1948), “A mathematical theory of communication”, Bell Syst. Tech. J 27, 379- 432.
Soliman, A. A., Abd-Ellah, A. H., Abou-Elheggag, N. A. and Ahmed, E. A. (2012), “ Modi-fied Weibull model: A Bayes study using MCMC approach based on progressive censoring data”, Reliability Engineering and System Safety.

Upadhyay, S. K. and Gupta, A. (2010), “ A Bayes analysis of modified Weibull distribu-tion via Markov chain Monte Carlo simulation”, Journal of Statistical Computation and Sim-ulation, 80(3), 241-254.

Xie, M. and Lai, C. D. (1996), “ Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function”, Reliability Engineering and System Safety, 52(1), 87-93.

Xie, M., Tang, Y. and Goh, T. N. (2002), “ A modified Weibull extension with bathtub shaped failure rate function”, Reliability Engineering and System Safety, 76(3), 279-285.

Zhang, T. and Xie, M. (2011), “ On the upper truncated Weibull distribution and its reli-ability implications”, Reliability Engineering and System Safety, 96(1), 194-200.