Measuring inaccuracies in the proportional hazard rate model based on extropy using a length-biased weighted residual approach

In this paper, we consider the concept of the residual inaccuracy measure and extend it to its weighted version based on extropy. The properties of this measure are studied, and the discrimination principle is applied in the class of proportional hazard rate models. A characterization problem for the proposed weighted extropy-inaccuracy measure is studied. Some alternative expressions are provided as well as upper and lower limits and various inequalities related to the proposed measure. Non-parametric estimators based on the kernel density estimation method and empirical distribution function for the proposed measure are obtained, and the performance of the estimators are also discussed using some simulation studies. Finally, two real datasets are applied to illustrate our provided estimators. In general, our study highlights the potential of the weighted residual inaccuracy using extropy as a powerful tool to improve the quality and reliability of data analysis and modeling across various disciplines. Researchers and practitioners can benefit from incorporating this measure into their analytical toolkit to enhance the accuracy and effectiveness of their work.