Marshall Olkin Exponentiated Dagum Distribution: Properties and Applications

Abstract

Abstract Marshall Olkin Exponentiated Dagum distribution (MOED) with four shape parameters and one scale parameter is proposed. Alternative expressions are derived for the newly proposed distribution to sort out lengthy calculations. Various properties of MOED are derived, including the measure of central tendency, the measure of dispersion, hazard rate and survival rate are also derived for the MOED. Moreover, the network properties are also derived, including moments, moment generating function, quantile function, median, and mean deviation random number generator. Estimation of parameters is done through MLE (Maximum likelihood estimation) method, and to assess the value of the proposed distribution, the performance of the parameter’s estimates is studied through Monte Carlo Simulation. Three real-life data sets are used to evaluate the application and to scrutinize the performance of MOED as compared to the Marshall Olkin Dagum (MOD) distribution, Exponentiated Dagum (ED) distribution, Dagum (D) distribution, Burr III distribution, Kumaraswamy Burr III (KBurr III) distribution, Kumaraswamy Log Logistic (KLL) distribution and Log Logistic (LL) distribution. Four information criteria are used to examine the performance of the MOED with other special cases. The results showed that the newly proposed distribution performs better than the compared distributions.

Keywords

• Marshal Olkin distribution
• Dagum distribution
• Exponentiated distribution
• Simulation
• Application