Topp-Leone Reduced Kies Distribution for Unit-Interval Data: Statistical Properties, Parameter Estimation, and Applications

This study introduces a two-parameter lifetime model named the Topp-Leone Reduced Kies (TLRK) distribution, which extends the Topp-Leone-G family by incorporating the Reduced Kies (RK) distribution as its baseline. The proposed distribution is designed for unit-interval data, such as proportions, rates, and reliability metrics. The TLRK distribution exhibits left-skewed, right-skewed, decreasing (or L-shaped), bathtub-shaped, and near-symmetric shaped density while the hazard rate function exhibits an increasing, and bathtub-shaped failure rates behaviour. Several statistical properties of the TLRK distribution, including moments, moment generating function, Rényi entropy, and order statistics are investigated. Seven distinct parameter estimation methods namely maximum likelihood, least squares, Cramér-von Mises, maximum product of spacings, Anderson-Darling, weighted least squares, and percentile-based estimation; are implemented and compared. A Monte Carlo simulation study evaluates the finite-sample performance of these estimators across varying sample sizes. The practical utility of the TLRK distribution is demonstrated through the analysis of two real unit-interval datasets (failure times of Kevlar strands and relief times of arthritic patients). Comparative analysis indicates that the TLRK distribution shows a favourable fit relative to some existing RK-based models, including the Reduced Kies, Extended Reduced Kies, Exponential Reduced Kies, and Marshall-Olkin Reduced Kies distributions.