A New Flexible Inverted Exponential Distribution: Characterization, Distinct Estimations and Applications

The study introduces a new probability distribution through integrating the Inverted Exponential distribution with the Type I Half Logistic Topp-Leone family of distributions. The resulting distribution, named; the Type I Half Logistic Topp-Leone Inverted Exponential Distribution (TIHLTLIE), avails the research environment with a new flexible framework for addressing diverse reliability and lifetime modeling. Several important mathematical properties of the proposed distribution, including moments (Ms), probability weighted moments (PWMs), and the moment generating function (MGF), are tractably obtained. Key reliability characteristics such as the hazard rate function, survival function and quantile function are derived and graphically visualized to demonstrate the behavior of the distribution. Parameter estimation is examined extensively through a comprehensive number of estimation approaches, namely, the Maximum Likelihood Estimation (MLE), Maximum Product of Spacings (MPS), Least Squares (LS), Weighted Least Squares (WLS), Cramér–von Mises (CVM), Anderson–Darling (AD), Percentile Estimation (PE), Method of Moments (MOM), L-Moments (L-MOM), Probability Weighted Moments (PWM), Trimmed L-Moments (TL-MOM), Wasserstein Distance Estimation (WDE), and Energy Distance Estimation (ENE). Rigorous Monte Carlo simulation study is performed to investigate the efficiency and consistency of these techniques via distinct sample sizes. The results demonstrate the performance exhibited in term of estimation accuracy across various scenarios by distance- and moment-based approaches, particularly the Energy Distance and L-moment-related estimators is superb. Finally, the applicability of the TIHLTLIE distribution is illustrated using two real-world datasets, where it provides a better fit than several comparators according to various information criteria. These findings demonstrate the applicability of the proposed distribution as a versatile distribution for modeling positively skewed data encountered in lifetime datasets.