A Heavy-Tailed QLindley Distribution for Modelling Skewed Lifetime Data

Lifetime data arising in engineering reliability, survival analysis, actuarial science, and environmental studies often exhibit substantial right-skewness, extreme observations, and heterogeneous hazard-rate structures. Classical lifetime distributions may not adequately capture these characteristics, thereby affecting risk assessment, reliability evaluation, and predictive performance. In this paper, we introduce the Heavy-Tailed QLindley (HTQL) distribution, a new two-parameter heavy-tailed extension of the QLindley model obtained through the New Family of Heavy-Tailed (NFHT) transformation. The proposed distribution provides greater flexibility for modelling positively skewed and heavy-tailed data while preserving analytical tractability. The HTQL model accommodates increasing, decreasing, bathtub-shaped, unimodal, and nearly constant hazard rate functions, making it suitable for applications in reliability analysis, survival studies, actuarial science, and environmental modelling. Several mathematical and statistical properties of the HTQL distribution are derived, including explicit expressions for the quantile function, ordinary and incomplete moments, order statistics, and reliability measures. Important tail-based risk measures such as Value-at-Risk, Tail Value-at-Risk, Tail Variance, Tail Variance Premium, and Expected Shortfall are also obtained. Parameter estimation is investigated using maximum likelihood, ordinary least squares, Cramér–von Mises, and Bayesian approaches, together with bootstrap confidence intervals. A Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the proposed estimators. The practical usefulness of the HTQL distribution is illustrated using three real-world datasets from pharmacokinetics, engineering reliability, and environmental studies. The empirical results show that the HTQL distribution provides highly competitive fits compared with several classical, Lindley-type, and heavy-tailed distributions. Overall, the proposed model constitutes a flexible and parsimonious alternative for modelling positive heavy-tailed data.