Huang and Oluyede Journal of Statistical Distributions and Applications 2014, 1:8 http://www.jsdajournal.com/content/1/1/8 RESEARCH Open Access Exponentiated Kumaraswamy-Dagum distribution with applications to income and lifetime data Shujiao Huang and Broderick O Oluyede* *Correspondence:
[email protected] Abstract Department of Mathematical A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) Sciences, Georgia Southern University, Statesboro, GA 30458, distribution is proposed and studied. This family includes several well known USA sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the sub-models are presented. Maximum likelihood estimates of the model parameters are obtained. Simulation studies are conducted. Examples and applications as well as comparisons of the EKD and its sub-distributions with other distributions are given. Mathematics Subject Classification (2000): 62E10; 62F30 Keywords: Dagum distribution; Exponentiated Kumaraswamy-Dagum distribution; Maximum likelihood estimation 1 Introduction Camilo Dagum proposed the distribution which is referred to as Dagum distribution in 1977. This proposal enable the development of statistical distributions used to fit empir- ical income and wealth data, that could accommodate heavy tails in income and wealth distributions.