A New Flexible Extension of the XLindley Distribution with Properties and Application on Income Tax and Carbon Fibers Data

A new and enhanced extension of the XLindley distribution termed the sized-biased XLindley distribution (SBXLD), has been introduced. This new model explores two specific variants: the length-biased XLindley distribution and the area-biased XLindley distribution. Various crucial properties such as moments, moment generating function, quantile function, survival, and hazard functions, mean residual life function, and Rényi entropy have been derived and extensively investigated. For parameter estimation, five distinct methods have been employed to estimate the model parameters. Through a comprehensive simulation study, the most effective estimation method has been identified. The applicability and efficiency of the SBXLD model have been demonstrated using two datasets from different domains. It has been observed that the SBXLD model effectively analyzed these datasets and yielded superior results compared to other competitive distributions under consideration.