International Journal of Pure and Applied Mathematics Volume 100 No. 2 2015, 309-335 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v100i2.11 P A ijpam.eu A NEW EXTENDED GAMMA GENERALIZED MODEL Ronaldo V. da Silva 1 § , Frank Gomes-Silva 2 , Manoel Wallace A. Ramos 3 , Gauss M. Cordeiro 4 1 Recife Military School Recife, 52070-080, BRAZIL 2 Department of Statistics and Informatics Federal Rural University of Pernambuco Recife, 52171-900, BRAZIL 3 Department of Mathematics Federal Institute of Para´ ıba Jo˜ ao Pessoa, 58015-020, BRAZIL 4 Department of Statistics Federal University of Pernambuco Recife, 50740-540, BRAZIL Abstract: We propose a new five-parameter extended gamma generalized model. Some special cases are discussed. We derive some mathematical prop- erties of the proposed distribution including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean devi- ations, reliability, order statistics and their moments and R´ enyi entropy. The method of maximum likelihood is used to estimate the model parameter. We ilustrate the potentiality of the new model with an application to a real data set. AMS Subject Classification: 60E05 Key Words: beta generalized, gamma distribution, exponentiated gamma distribution, exponentiated generalized gamma distribution, maximum likeli- hood estimation, moment Received: January 4, 2015 c  2015 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author