title: The McDonald exponentiated gamma distribution and its statistical properties.
abstract: In this paper, we propose a five-parameter lifetime model called the McDonald exponentiated gamma distribution to extend beta exponentiated gamma, Kumaraswamy exponentiated gamma and exponentiated gamma, among several other models. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment. We discuss estimation of the parameters by maximum likelihood and provide the information matrix.
  
  
  METHODS
  Primary 62N05; secondary 90B25.
authors.affiliation: Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451 Saudi Arabia.
authors.forename: Abdulhakim A
authors.initials: AA
authors.lastname: Al-Babtain
authors.affiliation: Department of Mathematics, University of Prishtina "Hasan Prishtina" & University of Mitrovica "Isa Boletini", Mother Teresa, Av=5, 10000 Prishtinë, Kosovo.
authors.forename: Faton
authors.initials: F
authors.lastname: Merovci
authors.affiliation: Institute of Statistical Studies and Research, Department of Mathematical Statistics, Cairo University, Cairo, Egypt.
authors.forename: Ibrahim
authors.initials: I
authors.lastname: Elbatal
keywords: Exponentiated gamma distribution; Maximum likelihood estimation; McDonald exponentiated gamma distribution; Moments; Order statistics