T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function

Abstract

Recently, different distributions have been generalized using the - R { Y } framework but the possibility of using Dagum distribution has not been assessed. The - R { Y } combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of - Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature.