Characterizations of the transmuted inverse Weibull distribution

We characterise the transmuted inverse Weibull distribution and compare it to many other generalizations of the two-parameter inverse Weibull distribution using the likelihood ratio test. Explicit expressions are derived for the quantile, moment generating function, entropies, mean deviation and order statistics. A bladder cancer application is presented to illustrate the proposed transmuted inverse Weibull distribution. References Arnold, B. C., Balakrishnan A. N. and Nagaraja H. N., A first course in order statistics, Wiley, New York, 1992. doi:10.1002/9781118150412 Aryal, G. R. and Tsokos, C. P., Transmuted Weibull distribution: A generalization of the Weibull Probability distribution. Europe. J. of Pure Appl. Math., 4(2):89–102, 2011. http://www.ejpam.com/index.php/ejpam/article/view/1170 Calabria, R. and Pulcini, G., On the maximum likelihood and least-squares estimation in the inverse Weibull distribution. Stat. Appl., 2:53–66, 1990. http://sa-ijas.stat.unipd.it/sites/sa-ijas.stat.unipd.it/files/53-66.pdf de Gusmao, F. R. S., Ortega, E. M. M. and Cordeiro, G. M., The generalized inverse Weibull distribution. Stat. Pap., 52:591–619, 2011. doi:10.1007/s00362-009-0271-3 Cordeiro, G. M., Gomes, A. E., da-Silva, C. Q. and Ortega, E. M. M., The beta exponentiated Weibull distribution. J. Stat. Comput. Sim., 83(1):114–138, 2013. doi:10.1080/00949655.2011.615838 Havrda, J. and Charvat, F., Quantification method in classification processes: concept of structural \(\alpha \)-entropy. Kybernetika, 3:30–35, 1967. http://www.kybernetika.cz/content/1967/1/30 Khan, M. S. and King, R., Transmuted modified Weibull distribution: A generalization of the modified Weibull probability distribution. Europe. J. of Pure Appl. Math., 6(1):66–88, 2013. http://www.ejpam.com/index.php/ejpam/article/view/1606 Khan, M. S. and King, R., Transmuted generalized inverse Weibull distribution. J. Appl. Stat. Sci., 20(3):15–32, 2013. https://www.novapublishers.com/catalog/product_info.php?products_id=47370 Keller, A. Z., Kamath A. R. R. and Perera, U. D., Reliability analysis of CNC machine tools. Reliab. Eng., 3:449–473, 1982. doi:10.1016/0143-8174(82)90036-1 Kaplan, E. L. and Meier, P., Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc., 53(282):457–481, 1958. doi:10.1080/01621459.1958.10501452 Lee, E. T. and Wang, J. W., Statistical Methods for Survival Data Analysis. Wiley, New York, 2003. doi:10.1002/0471458546 Liu, C.-C., A Comparison between the Weibull and Lognormal Models used to Analyze Reliability Data. PhD Thesis University of Nottingham, 1997. Renyi, A., On measures of information and entropy. Proc. Fourth Berkeley Symp. on Math. Statist. and Prob. 1:547–561, 1961. http://projecteuclid.org/euclid.bsmsp/1200512181 The R Project for Statistical Computing, Vienna, Austria, 2014. http://www.R-project.org Shaw, W. T. and Buckley, I. R. C., 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/0901.043