θ-Weighted mixture distribution: the Weibull-Lomax case

Abstract

IntroductionThis article introduces a new family of weighted mixture distributions, referred to as θ-WM. The θ-WM family is generated by combining two distributions weighted by a parameter θ, offering notable flexibility to model a wide range of complex phenomena. A special case study of the θ-weighted mixture distribution of Weibull-Lomax (θ-WMWLx) is included, resulting from the combination of Weibull and Lomax distributions.MethodsThe research thoroughly examines the reliability and statistical properties of the θ-WMWLx distribution. Key aspects such as stochastic dominance, survival and hazard functions, mean residual life, and moments are addressed. The maximum likelihood method is used to estimate unknown parameters.ResultsThe research findings show that the θ-WMWLx distribution provides a superior fit compared to competing distributions. The analyses are validated using three real datasets, demonstrating the effectiveness of the proposed distribution.DiscussionThe θ-WMWLx distribution stands out for its ability to model complex phenomena with high precision. Validation with real data confirms that the proposed distribution offers a better fit than existing distributions, highlighting its utility and applicability in various statistical analysis contexts.