The Q-Lindley Distribution: Goodness-of-Fit Tests, Modeling, Inference, and Applications

This paper introduces the Q-Lindley distribution (QLD), a new one-parameter model for lifetime and reliability data derived from the affine exponential family. We derive its main statistical properties and estimate the parameter using maximum likelihood. The performance of the QLD is evaluated using Monte Carlo simulations and four real datasets, and its fit is compared to several classical and Lindley-type distributions. Model selection criteria and Goodness-of-Fit statistics indicate that the QLD provides competitive or superior performance despite its simple structure. These results suggest that the QLD is a useful addition to the family of lifetime distributions.