Truncated power Chris–Jerry distribution: Classical estimation methods and modeling to survival data

In many real-world scenarios, a truncated distribution arises when the domain of the parent distribution is restricted to a smaller region. This paper presents the truncated power Chris-Jerry distribution (TPC-JD), a novel flexible two-parameter truncated distribution with a domain [0, 1]. The introduction of a new distribution opens up a wide range of options and possibilities, making it possible to choose the model that best fits certain data and research goals. The associated probability density function is very adaptable as it may take on unimodal, reversed j-shaped, and various asymmetric patterns. The corresponding hazard rate function indicates that data with U- or j-shaped failure rates may be adapted by the TPC-JD. The mathematical computation of a number of statistical characteristics is given. Several estimation techniques, including twelve traditional approaches, are investigated to evaluate and compare the behavior of parameter estimates for the TPC-JD. To identify the optimal estimation strategy, a simulation study is conducted. The simulation results indicate that the percentile method is the optimal technique to estimate the quality of TPC-JD estimators. In addition, we investigate two real-world survival data sets using the TPC-JD, showing its better performance compared to some competitors.