Modeling With the Inverse Unit New XLindley Distribution: Properties and Real‐World Applications

ABSTRACT This paper proposes a novel form of the unit new XLindley distribution, which is derived by incorporating the idea of inverse transformation of the cumulative distribution function. The derived distribution is defined on the positive real line and it exhibits a different range of shapes. We also discuss some important statistical properties of the proposed model, including moments, moment‐generating function, survival and hazard rate functions, quantiles, order statistics, etc., to present a comprehensive theoretical framework. In addition to these, fifteen different estimation methods are employed for conducting the parameter estimation for the new distribution. Besides, a simulation study is performed to evaluate their behaviors using some measures like bias, mean squared error, relative error, and absolute differences. Besides, the usefulness and utility of the newly proposed distribution are checked through real‐life applications via some practical datasets. This practical application is conducted by comparing the new distribution with some other existing counterparts in terms of the value of some model selection criterion.