Extended Exponentiated Chen Distribution: Mathematical Properties and Applications

  • Zohreh Zamani Shahid Bahonar University, Iran
  • Mahmoud Afshari Associate Professor. Persian Gulf University, 7516913798, Iran
  • H. Karamikabir Persian Gulf University, Iran
  • M. Alizadeh Persian Gulf University, Iran
  • M. Masoom Ali Ball State University, USA
Keywords: Chen distribution, Exponentiated Chen distribution, Moments, Mean residual life, Mean past lifetime, Maximum likelihood estimation


In this paper, we introduce a new four-parameter distribution which is called Extended Exponentiated Chen (EE-C) distribution. Theoretical properties of this model including the hazard function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, order statistics and asymptotic properties are derived and studied. The maximum likelihood estimation technique is used to estimate the parameters of this model. The estimation of the model parameters by Least squares, Weighted Least Squares, Crammer-von-Mises, Anderson-Darling and right-tailed Anderson-Darling methods are also briefly introduced and numerically investigated. Moreover, simulation schemes are derived. At the end, three applications of the model with two real data sets are presented for the illustration of the flexibility of the proposed distribution.


M. Alizadeh, M. Afshari, B. Hosseini, and T.G. Ramires, Extended Exp-G family of distributions: Properties and Applications, Communication in Statistics-Simulation and Computation, vol. 49(7), pp. 1730–1745, 2020.

A. Alzaatreh, F. Famoye, and C. Lee, The gamma-normal distribution: Properties and applications, Computational Statistics and Data Analysis, vol 69, pp. 67–80, 2014.

T. W. Anderson, and D. A. Darling, Asymptotic theory of certain” goodness of fit” criteria based on stochastic processes , The annals of mathematical statistics, pp. 193–212, 1952.

G. R. Aryal, and C. P. Tsokos, On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Applications, vol. 71, pp. 1401–1407, 2009.

Y. P. Chaubey, and R. Zhang, An extension of Chen’s family of survival distributions with bathtub shape or increasing hazard rate function, Communications in Statistics-Theory and Methods, vol. 44, pp. 4049–4064, 2015

Z. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics and Probability Letters, vol. 49, pp. 155–161, 2000.

K. Choi, and W. Bulgren, An estimation procedure for mixtures of distributions , Journal of the Royal Statistical Society. Series B (Methodological), pp. 444–460, 1968.

G. M. Cordeiro, and M. de Castro, A new family of Generalized distributions, Journal of Statistical Computation and Simulation, vol. 81, pp. 883–898, 2011.

G. M. Cordeiro, S. Nadarajah,and E. M. Ortega, The Kumaraswamy Gumbel distribution, Statistical Methods and Applications, vol. 21, pp. 139–168, 2012.

S. Dey, J. Mazucheli and S. Nadarajah, Kumaraswamy distribution: different methods of estimation, Computational and Applied Mathematics, pp. 1–18, 2017.

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

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

A. J. Gross, and V. A. Clark, Survival distributions: Reliability Applications in the Biomedical Sciences. John Wiley and Sons, New York, 1975.

R. C. Gupta, P. L. Gupta, and R. D. Gupta, Modeling failure time data by Lehman alternatives Communications in Statistics-Theory and methods, vol. 27, pp. 887–904, 1998.

K. K. Jose, Marshall-Olkin family of distributions and their applications in reliability theory, time series modeling and stress-strength analysis, Proc. ISI 58th World Statist. Congr Int Stat Inst, 21st-26th August, 3918–3923, 2011.

H. Karamikabir, M. Afshari, H. Yousef, M. Alizadeh, and G. G. Hamedani, The Weibull Topp-Leone Generated Family of Distributions: Statistical Properties and Applications, Journal of The Iranian Statistical Society, vol. 19(1), pp. 121–161, 2020.

H. Karamikabir, M. Afshari, M. Alizadeh, and G. G. Hamedani, A new extended generalized Gompertz distribution with statistical properties and simulations, Communications in Statistics - Theory and Methods, Published online, vol. 50(2), pp. 251–279, 2021.

M. S. Khan, R. King, and I. L. Hudson, A new three parameter transmuted Chen lifetime distribution with application, Journal of Applied Statistical Science, vol. 21, pp. 239–259, 2013.

M. S. Khan, R. King, and I. L. Hudson, Transmuted exponentiated Chen distribution with application to survival data ANZIAM Journal, vol. 57, pp. 268–290, 2016.

A. W. Marshall, and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families Biometrika, vol. 84, pp. 641–652, 1997.

M. mozafari, M. Afshari, M. Alizadeh, and H. Karamikabir, The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations, Statistics, Optimization and Information Computing, vol. 7(1), pp. 211–234, 2019.

A. Renyi, On measures of entropy and information. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability–I, University of California Press, Berkeley, pp. 547–561, 1961.

C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol. 27, pp. 379–432, 1948.

J. J. Swain, S. Venkatraman, and J. R. Wilson, Least-squares estimation of distribution functions in johnson’s translation system, Journal of Statistical Computation and Simulation, vol. 29, pp. 271– 297, 1988.

How to Cite
Zamani, Z., Afshari, M., H. Karamikabir, M. Alizadeh, & M. Masoom Ali. (2021). Extended Exponentiated Chen Distribution: Mathematical Properties and Applications. Statistics, Optimization & Information Computing, 10(2), 606-626. https://doi.org/10.19139/soic-2310-5070-1098
Research Articles