A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms

In this study, a new one-parameter Log-XLindley distribution is proposed to analyze the proportion data. Some of its statistical and reliability properties, including moments with associated measures, hazard rate function, reversed hazard rate, stress strength reliability, and mean residual life function, are investigated in closed forms which help the researchers for modeling data in a small CPU time. It is found that the density function of the introduced distribution can be used as a statistical tool to model asymmetric data. Moreover, the failure rate function can be utilized to model different types of failures, including increasing, bathtub, and J-shaped. The model parameter is estimated using various estimation approaches to get the best estimator to help us in modeling the real data in a good way with high accuracy. A Monte-Carlo simulation study for different sample sizes is performed to assess the performance of the estimations based on some statistical criteria. Finally, two distinctive data sets from SC16 and P3 algorithms, “estimating unit capacity factors,” are analyzed to illustrate the flexibility of the new model.