The McDonald exponentiated gamma distribution and its statistical properties

Abdulhakim A Al-Babtain; Faton Merovci; Ibrahim Elbatal

doi:10.1186/2193-1801-4-2

The McDonald exponentiated gamma distribution and its statistical properties

Springerplus. 2015 Feb 12;4(1):2. doi: 10.1186/2193-1801-4-2. eCollection 2015.

Authors

Abdulhakim A Al-Babtain¹, Faton Merovci², Ibrahim Elbatal³

Affiliations

¹ Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451 Saudi Arabia.
² Department of Mathematics, University of Prishtina "Hasan Prishtina" & University of Mitrovica "Isa Boletini", Mother Teresa, Av=5, 10000 Prishtinë, Kosovo.
³ Institute of Statistical Studies and Research, Department of Mathematical Statistics, Cairo University, Cairo, Egypt.

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.

Ams subject classification: Primary 62N05; secondary 90B25.

Keywords: Exponentiated gamma distribution; Maximum likelihood estimation; McDonald exponentiated gamma distribution; Moments; Order statistics.