Zero-inflated discrete Lindley distribution: Statistical and reliability properties, estimation techniques, and goodness-of-fit analysis

This study introduced a two-parameter zero-inflated discrete random variable distribution designed to model failure profiles in zero-inflated, dispersed datasets, commonly found in biological engineering and reliability analysis. The proposed distribution combined traditional count models, such as Poisson, Lindley, or negative binomial, with a probability mass at zero, providing a robust framework for addressing excess zeros and the underlying dispersion of data. The mathematical foundation of the distribution was derived with an emphasis on its statistical and reliability properties. The probability mass function was applicable to datasets with asymmetric dispersion and varying kurtosis structures. In addition, the hazard rate function was used to analyze failure rate behaviors, capturing patterns such as increasing, decreasing, and bathtub-shaped failure rates, often encountered in real-world datasets. Also, characterization of the proposed distribution was explored based on conditional expectation and the hazard rate function. Parameter estimation techniques were proposed, alongside computational simulations, to identify the most consistent estimators for data modeling. The goodness of fit of the proposed model was rigorously evaluated by comparing it with existing count models, demonstrating its superior ability to model zero-inflated, overdispersed data. Finally, the practical application of the new distribution was demonstrated using real-life biological engineering datasets, highlighting its effectiveness and flexibility in modeling complex zero-inflated data across various failure profiles and reliability contexts.