The Complementary Generalized Transmuted Poisson-G Family of Distributions

  • Morad Alizadeh
  • Haitham M. Yousof
  • Ahmed Z. Afify Department of Statistics, Mathematics and Insurance, Benha University
  • Gauss M. Cordeiro
  • M. Mansoor


We introduce a new class of continuous distributions called the complementary generalized transmuted Poisson-G family, which extends the transmuted class pioneered by Shaw and Buckley (2007). We provide some special models and derive general mathematical properties including quantile function, explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies and order statistics. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the new family is illustrated by means of two applications to real data sets.


Afify, A. Z., Alizadeh, M., Yousof, H. M., Aryal, G. and Ahmad, M. (2016a). The transmuted geometric-G family of distributions: theory and applications. Pakistan Journal of Statistics, 32, 139-160.

Afify A. Z., Cordeiro, G. M., Yousof, H. M., Alzaatreh, A. and Nofal, Z. M. (2016b). The Kumaraswamy transmuted-G family of distributions: Properties and Applications. Journal of Data Science, 14, 245-270.

Al-Babtain, A., Fattah, A. A., Ahmed, A. N., and Merovci, F. (2015). The Kumaraswamy transmuted exponentiated modified Weibull distribution. Communications in Statistics-Simulation and Computation, forthcoming.

Alexander, C., Cordeiro, G.M., Ortega, E. M. M. and Sarabia, J.M. (2012). Generalized beta generated distributions. Computational Statistics and Data Analysis, 56, 1880-1897.

Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. M. M., Pescim, R. R. (2015). A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepa Journal of Mathematics and Statistics, forthcomig.

Alzaatreh, A., Lee, C. and Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71, 63-79.

Cakmakyapan, S. and Kadilar, G. O. (2014). A new customer lifetime duration distribution: the Kumaraswamy Lindley Distribution. International Journal of Trade, Economics and Finance, 5, 441-444.

Cordeiro, G. M, Alizadeh, M, Tahir, M. H., Mansoor, Bourguignon, M. and Hamedani, G. G. (2015). The beta odd log-logistic generalized family of distributions. Hacettepe Journal of Mathematics and Statistics, forthcoming.

Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-898.

Eugene, N., Lee, C. and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31, 497-512.

Flores, J., Borges, P., Cancho, V. G. and Louzada, F. (2013). The complementary exponential power series distribution. Brazilian Journal of probability and statistics, 27, 565-584.

Ghitany, M. E., Al-Mutairi, D.K., Balakrishnan, N. and Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, 20-33.

Jorgensen, B. (1982). Statistical properties of the generalized inverse Gaussian distribution. New York: Springer-Verlag.

Khan, M. S. and King, R. (2013). Transmuted modified Weibull distribution: a generalization of the modified Weibull probability distribution. European Journal of Pure and Applied Mathematics, 6, 66-88.

Lee, E. and Wang, J. (2003). Statistical Methods for Survival Data Analysis. John Wiley and Sons, New York.

Marshall, A. N. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families. Biometrika, 84, 641-652.

Mead, M. E. and Afify, A. Z. (2016). On five-parameter Burr XII distribution: properties and applications. South African Statistical Journal, forthcoming..

Merovci, F. and Elbatal, I. (2013). The McDonald modified Weibull distribution: properties and applications. arXiv preprint arXiv:1309.2961.

Merovci, F. and Sharma, V. K. (2014). The beta Lindley distribution: properties and applications. Journal of Applied Mathematics, 51, 1-10.

Nichols, M. D. and Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International, 22, 141-151.

Nofal, Z. M., Afify, A. Z., Yousof, H. M. and Cordeiro, G. M. (2015). The generalized transmuted-G family of distributions. Communications in Statistics-Theory and Methods, forthcoming.

Shaw, W. T. and Buckley, I. R. C. (2007). The alchemy of probability distributions: beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434.

Yousof, H. M., Afify, A. Z., Alizadeh, M., Butt, N. S., Hamedani, G. G. andAli, M. M. (2015). The transmuted exponentiated generalized-G family of distributions. Pakistan Journal of Statistics and Operations Research, 11, 441-464.

Zografos K. and Balakrishnan, N. (2009) On families of beta and generalized gamma generated distributions and associated inference. Statistical Methodology, 6, 344-362.

How to Cite
Alizadeh, M., Yousof, H. M., Afify, A. Z., Cordeiro, G. M., & Mansoor, M. (2018). The Complementary Generalized Transmuted Poisson-G Family of Distributions. Austrian Journal of Statistics, 47(4), 60-80.