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 \ (\) -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/productᵢnfo. php? productsᵢd=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. 0434