Transmuted exponentiated Chen distribution with application to survival data

Abstract

This article considers an extension of the exponentiated Chen distribution based on the quadratic rank transmutation map technique. Some structural properties of the transmuted exponentiated Chen distribution are discussed. The estimation procedure is performed using the method of maximum likelihood. Finally, the flexibility of the new distribution is illustrated using strengths of glass fibres data and nicotine in cigarettes data. References

• G. R. Aryal and C. P. Tsokos. Transmuted Weibull distribution: A generalization of the Weibull probability distribution. Euro. J. Pure Appl. Math., 4(2):89–102, 2011. http://www.ejpam.com/index.php/ejpam/article/view/1170
• Z. Chen. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stats. Prob. Lett., 49:155–161, 2000. doi:10.1016/S0167-7152(00)00044-4
• Y. P. Chaubey and R. Zhang. An extension of Chen's family of survival distributions with bathtub shape or increasing hazard rate function. Commun. Stat. A: Theor., 44(19):4049–4064, 2015. doi:10.1080/03610926.2014.997357
• M. S. Khan and R. King. Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Euro. J. Pure Appl. Math., 6(1):66–88, 2013. http://www.ejpam.com/index.php/ejpam/article/view/1606
• M. S. Khan, R. King and I. Hudson. Characterizations of the transmuted inverse Weibull distribution. ANZIAM J, 55:C197–C217, 2014. doi:10.21914/anziamj.v55i0.7785
• M. S. Khan and R. King. A new class of transmuted inverse Weibull distribution for reliability analysis. Am. J. Math. Manage. Sci.. 33(4):261–286, 2014. doi:10.1080/01966324.2014.929989
• M. S. Khan, R. King and I. Hudson. A new three parameter transmuted Chen lifetime distribution with application. J. Appl. Stat. Sci., 21(3) 2015. https://www.novapublishers.com/catalog/product_info.php?products_id=54720
• F. Merovci. Transmuted Rayleigh distribution. Austrian J. Stat., 42(1):21–31, 2013. http://www.ajs.or.at/index.php/ajs/article/view/vol42,%20no1-2
• R. L. Smith and J. C. Naylor. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. J. Roy. Stat. Soc. C–App., 36:358–369, 1987. doi: 10.2307/2347795
• W. T. Shaw and I. R. C. Buckley. The alchemy of probability distributions: Beyond Gram–Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Technical report, 2009. http://arxiv.org/abs/0901.0434
• Federal Trade Commission (USA). Results of tar, nicotine and carbon monoxide testing for 1,249 varieties of domestic cigarettes sold in 1995. File No. 962 3099, Jan. 1998. https://www.ftc.gov/news-events/press-releases/1998/01/results-tar-nicotine-and-carbon-monoxide-testing-1249-varieties