# Exponentiated Extended Chen Distribution: Regression Model and Estimations

### Abstract

In this paper, we introduce a new four-parameter generalized version of the Chen model called the exponentiated extended Chen distribution. Some results about the reliability characteristics of hazard rate function as well as some mathematical properties are provided. The maximum likelihood estimators and five approaches based on the concept of minimum spacing distance estimators are given for estimation of the model parameters and their performances in estimating of parameters are compared by means of Monte Carlo simulations. Also, a multiple regression model with the censored data based on proposed distribution is introduced.### References

Afify, A. Z., Alizadeh, M., Zayed, M., Ramires, T. G., and Louzada, F., The odd log-logistic exponentiated Weibull distribution: Regression modeling, properties, and applications, Iranian Journal of Science and Technology, Transactions A: Science, vol. 42(4), pp. 2273-2288, 2018.

Chaubey, Y. P. and Zhang, R., 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(19), pp. 4049-4064, 2015.

Chen, Z., A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, vol. 49(2), pp. 155-161, 2000.

Cordeiro, G. M. and de Castro, M., A new family of generalized distributions, Journal of statistical computation and simulation, vol.81(7), pp. 883-898, 2011.

Cooray, K. and Ananda, M. M., A generalization of the half-normal distribution with applications to lifetime data, Communications in Statistics-Theory and Methods, vol. 37(9), pp. 1323-1337, 2008.

Dey, S., Kumar, D., Ramos, P. L., and Louzada, F., Exponentiated Chen distribution: Properties and estimation, Communications in Statistics-Simulation and Computation, vol. 46(10), pp. 8118-8139, 2017.

Feigl, P. and Zelen, M., Estimation of exponential survival probabilities with concomitant information, Biometrics, vol. 21(4), pp. 826-838, 1965.

Gl¨anzel,W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory, vol. B, Reidel, Dordrecht, pp. 75-84, 1987.

Johnson, N. L., Kotz, S., and Balakrishnan, N. , Continuous Univariate Distributions, John Wiley & Sons, New York, second edition, 1995.

Kazemi, M. R., Jafari, A. A., and Tahmasebi, S. , An extension of the generalized linear failure rate distribution, Communications in Statistics-Theory and Methods, vol. 46(16), pp. 7916-7933, 2017.

Kazemi, M. R., Jafari, A. A., and Tahmasebi, S. , A Modification of the Gompertz Distribution Based on the Class of Extended-Weibull Distributions, Journal of Statistical Theory and Applications, vol. 19(4), pp. 472-480, 2021.

Khan, M. S., King, R., and Hudson, I., A new three parameter transmuted Chen lifetime distribution with application, Journal of Applied Statistical Science, vol. 21(3), pp. 239-259, 2013.

Kundu, D. and Gupta, R. D. , An extension of the generalized exponential distribution, Statistical Methodology, vol. 8(6), pp. 485-496, 2011.

Pescim, R. R., Dem´etrio, C. G., Cordeiro, G. M., Ortega, E. M., and Urbano, M. R. , The beta generalized half-normal distribution, Computational statistics & data analysis, vol. 54(4), pp. 945-957, 2010.

Ramires, T., Ortega, E., Cordeiro, G., and Hamedani, G. G. , The beta generalized half-normal geometric distribution, Studia Scientiarum Mathematicarum Hungarica, vol. 50(4), pp. 523-554, 2013.

Smith, R. L. and Naylor, J. C. , A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution, Applied Statistics, vol. 36(3), pp. 358-369, 1987.

Torabi, H. , A general method for estimating and hypotheses testing using spacing, Journal of Statistical Theory and Applications, vol. 8(2), pp. 163-168, 2008.

Torabi, H. , A new method for hypotheses testing using spacings, Statistics & Probability Letters, vol. 76(13), pp. 1345-1347, 2006.

Torabi, H., Bagheri, F. L. and Mahmoudi, E. , Estimation of parameters for the MarshallOlkin generalized exponential distribution based on complete data, Mathematics and Computers in Simulation, vol. 146, pp. 177-185, 2018.

Torabi, H., Bagheri, F. L. and Mahmoudi, E. , Estimation of parameters for the MarshallOlkin generalized exponential distribution based on complete data, Mathematics and Computers in Simulation, vol. 146, pp. 177-185, 2018.

*Statistics, Optimization & Information Computing*,

*10*(3), 710-724. https://doi.org/10.19139/soic-2310-5070-1090

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