An improved version of ZLindley distribution with mathematical properties and applications

The growing complexity of contemporary lifetime data necessitates the advancement of more adaptable probability models. To meet this demand, an advanced extension of the ZLindley distribution called the size-biased ZLindley (SBZL) distribution has been developed via a weighted approach. This new modification enhances the flexibility of the standard distribution by refining its functional shape and enabling it to model the most probable form of the hazard rate function effectively. The new model includes various distinct sub-models based on its parameter values. Here we discussed and studied their two variants: the length-biased ZLindley and area-biased ZLindley distributions. Key properties, such as moments, mean residual life function, moment-generating function, and entropy, along with their associated computational features, were described in depth. To estimate the model parameters, four different estimation methods were applied, and a detailed simulation study identified the most effective approach. The practicality and efficiency of the SBZL distribution model were validated using datasets from two distinct fields, where it was found to deliver superior results compared to other competing distributions. We also utilized a Bayesian approach to analyze both datasets.