Research Article The Exponentiated Gumbel Type-2 Distribution: Properties and Application I. E. Okorie, 1 A. C. Akpanta, 2 and J. Ohakwe 3 1 School of Mathematics, University of Manchester, Manchester M13 9PL, UK 2 Department of Statistics, Abia State University, PMB 2000, Uturu, Abia State, Nigeria 3 Department of Mathematics & Statistics, Faculty of Sciences, Federal University, Otuoke, PMB 126, Yenagoa, Bayelsa, Nigeria Correspondence should be addressed to I. E. Okorie; idika.okorie@postgrad.manchester.ac.uk Received 17 May 2016; Accepted 10 July 2016 Academic Editor: Niansheng Tang Copyright © 2016 I. E. Okorie et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduce a generalized version of the standard Gumble type-2 distribution. Te new lifetime distribution is called the Exponentiated Gumbel (EG) type-2 distribution. Te EG type-2 distribution has three nested submodels, namely, the Gumbel type- 2 distribution, the Exponentiated Fr´ echet (EF) distribution, and the Fr´ echet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. Te usefulness and fexibility of the Exponentiated Gumbel (EG) type-2 distribution were illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better ft to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. Te EG type-2 distribution is therefore recommended for efective modelling of lifetime data. 1. Introduction Te Gumbel distribution, also known as the type-1 extreme value distribution, has received signifcant research attention, over the years particularly, in extreme value analysis of extreme events. For a review of the recent developments and applications of the Gumbel distribution, see Pinheiro and Ferrari [1]. Tere is no question that, before now, the Gumbel type-2 distribution is not popularly used in statistical modelling and the reason may not be far from its lack of fts in data modelling. Generally, standard probability distributions are well known for their lack of fts in modelling complex data sets. On this note, users of this distributions across various felds in general and statistics and mathematics in particular have been fantastically motivated to developing sophisticated probability distributions from the existing ones. Exponentiated distributions have been introduced to solve the problem of lack of fts that is commonly encountered when using the standard probability distributions for mod- elling complex data sets. Results from this advancement have frequently been proven more reasonable than the one based on the standard distributions. Exponentiating distributions are indeed a powerful technique in statistical modelling that ofers an efective way of introducing an additional shape parameter to the standard distribution to achieve robustness and fexibility. Tis method of generaliz- ing probability distributions is traceable to the work of Gupta et al. [2] who introduced the exponentiated exponential (EE) distribution as a generalized form of the standard exponential distribution by simply raising the cumulative density function (cdf) to a positive constant power. Ever since the introduction of the EE distribution, exponentiated distributions have achieved reasonable feats in modelling data sets from various complex phenomena. A good number of standard probability distributions have their correspond- ing exponentiated versions. Gupta et al. [2] introduced the Exponentiated Weibull distribution as a generalization of the standard Weibull distribution. Nadarajah and Kotz [3] modifed the method by Gupta et al. [2] and introduced the Exponentiated Fr´ echet distribution as a generalization of the standard Fr´ echet distribution. Using the same method in Nadarajah and Kotz [3], Nadarajah [4] introduced the Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2016, Article ID 5898356, 10 pages http://dx.doi.org/10.1155/2016/5898356