A New Generalized Log-Logistic Erlang Truncated Exponential Distribution with Applications


We introduce a new distribution via the Marshall-Olkin generator called
the Marshall-Olkin Log-logistic Erlang-Truncated Exponential (MOLLoGETE) distribution.  Some structural properties of the distribution including series expansion of the density function, sub-models, hazard function, moments, conditional moments, mean deviations, distribution of order statistics, R´enyi entropy and maximum likelihood estimates are presented.  The new density function is an infinite linear combinations of Burr XII-Erlang-Truncated Exponential distributions.  The new generalization is applied to real data sets to evaluate the model performance.

DOI Code: 10.1285/i20705948v13n2p293

Keywords: Marshall-Olkin,Generalized distribution, Erlang Truncated Ex- ponential distribution, Maximum Likelihood Estimation.


Barreto-Souza, W., Lamonte, A. J., and Cordeiro, G. M. (2013). General Results for the Marshall and Olkin’s Family of Distributions Annals of the Brazilian Academy of Sciences 85(1), 3–21.

Chambers, J., Cleveland, W., Kleiner, B. and Tukey, J., (1983). Graphical Methods for Data Analysis. Chapman and Hall, London.

Chen, G. and Balakrishnan, N., (1995). A General Purpose Approximate Goodness-of-fit Test. Journal of Quality Technology 27, 154–161.

Cordeiro G. M. and Lemonte A. J., (2011). On the Marshall-Olkin Extended Weibull Distribution Stat. Paper 54, 333–353.

El-Alosey A. R., (2007). Random Sum of New Type of Mixture of Distribution Inter- national Journal of Statistics and Systems, 2, 49–57.

Gleaton, J. and Lynch, J., (2006). Properties of Generalized Log-logistic Families of Lifetime Distributions, Journal of Probability and Statistical Sciences, 4(1), 51–64.

Gradshteyn, I. S., and Ryzhik, I., M., (2000). Table of Integrals, Series and Products, Academic Press, San Diego.

Lee, C., Famoye, F., and Olumolade, O., (2007). Beta-Weibull Distribution: Some Properties and Applications, Journal of Modern Applied Statistical Methods, 6, 173– 186.

Ghitany, M. E., Atieh, B., and Nadarajah, S., (2008). Lindley Distribution and Its Application, Mathematics and Computers in Simulation, 78, 493–506.

Ghitany, M.E, AL-Hussaini, E. K and AL-Jarallah.,(2005). Marshall-Olkin Extended Weibull Distribution and Its Application to Censored Data, Journal of Applied Statis- tics, 32(10),


Lepetu, L., Oluyede, B. O., Makubate, B., Foya, S. and Mdlongwa, P., (2017). Marshall- Olkin Log-Logistic Extended Weibull Distribution : Theory, Properties and Applications, Journal of Data Science, 15, 691–722.

Marshall, A. W. and Olkin, I., (1997). A New Method for Adding a Parameter to a Family of Distributions with Application to the Exponential and Weibull Families, Biometrika, 84, 641–652.

Nichols, M.D. and Padgett, W.J., (2006). A Bootstrap Control chart for Weibull Percentiles, Quality and Reliability Engineering International, 22, 141–151.

Oluyede, B. O., Huang, S. and Pararai, M., (2014). A New Class of Generalized Dagum Distribution with Applications to Income and Lifetime Data, Journal of Statistical and Econometric Methods,

(2), 125–151.

Oluyede, B. O., Foya, S., Warahena-Liyanage, G. and Huang, S., (2016). The Log- logistic Weibull Distribution with Applications to Income and Lifetime Data, Austrian Journal of Statistics, 45,


R Development Core Team, (2011). A Language and Environment for Statistical Computing R Foundation for Statistical Computing, Vienna, Austria.

R´enyi, A., (1960). On Measures of Entropy and Information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 547 – 561.

Santos-Nero, M., Bourguignon, M., Zea, L. M., Nascimento, A. D. C. and Cordeiro, G. M., (2014). The Marshall-Olkin Extended Weibull Family of Distributions, Journal of Statistical Distributions

and Applications, 1–9.

Zhang, T. and Xie, M., (2007). Failure Data Analysis with Extended Weibull Distribution, Communications in Statistics - Simulations and Computations, 36, 579–592.

Zografos, K. and Balakrishnan, N., (2009). On Families of beta- and Generalized Gamma-Generated Distribution and Associated Inference, Journal of Statistical Method, 6, 344-362.

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