θ-Weighted mixture distribution: the Weibull-Lomax case - Carvajal-Muquillaza, Cristian; Manríquez, Ronald; Cabrera, Eduardo (Frontiers in Applied Mathematics and Statistics, 2024)
This article introduces a new family of weighted mixture distribution, which is referred to as θ-WM. The θ-WM family is generated by combining two distributions weighted by the parameter θ. This family provides remarkable flexibility that allows modeling a wide range of complex phenomena. As a special case study, the θ-weighted mixture distribution of Weibull Lomax (θ-WMWLx) is included, resulting from the combination of Weibull and Lomax distributions. The research thoroughly examines the reliability and statistical properties of θ-WMWLx, shedding light on crucial aspects such as stochastic dominance, survival and hazard functions, mean residual life, and moments. Additionally, the maximum likelihood method is employed to estimate unknown parameters. Finally, the results are validated using two real datasets, demonstrating that the proposed distribution provides a better fit than two other distributions.