77 Vol.5.Issue.2.2017 (April-June) ©KY PUBLICATIONS THE GENERALIZED WEIBULL-GUMBEL DISTRIBUTION Innocent Boyle ERAIKHUEMEN 1 , Terna Godfrey IEREN 2 1 Department of Mathematics and Computer Science, Benson Idahosa University Benin-city, Nigeria ieraikhuemen@biu.edu.ng 2 Department of Statistics, Ahmadu Bello University Zaria, Nigeria ternagodfrey@gmail.com ABSTRACT This paper studies another generalization of the Gumbel distribution known as the Generalized Weibull-Gumbel distribution useful for modeling lifetime data. The mathematical properties of the new distribution are provided. The explicit expressions for its quantile, survival, and hazard functions were studied. Some plots of the distribution indicate that the Generalized Weibull- Gumbel distribution can take various shapes such as symmetrical, left- skewed, right-skewed etc. This fact implies that the Generalized Weibull- Gumbel distribution can be very useful for data sets under various shapes. The implications of the plots for the survival and hazard functions means that the Generalized Weibull-Gumbel distribution (GWGD) will be appropriate in modeling time or age-dependent events, where survival rate decreases with time and failure increases with time or age. The method of maximum likelihood is used for estimating the model parameters and the density function for the minimum and maximum order statistics are also derived. We finally illustrate the usefulness of the proposed model. Keywords: Gumbel Distribution, Reliability analysis, Maximum likelihood estimation, order statistics and Generalized Weibull-Gumbel distribution. 1 Background The Gumbel distribution is a very popular statistical model due to its wide applicability. An extensive list of the Gumbel model applications can be obtained in Kotz and Nadarajah (2000). Some applications of the Gumbel model include: climate modeling, global warming problems, offshore modeling, rainfall and wind speed modeling Nadarajah (2006). The applications of this model can also be found in various areas of engineering, suĐh as flood frequency analysis, network, nuclear, BULLETIN OF MATHEMATICS AND STATISTICS RESEARCH A Peer Reviewed International Research Journal http://www.bomsr.com RESEARCH ARTICLE Email:editorbomsr@gmail.com