On the T-Topp-Leone family of distributions for lifetime data analysis

This study introduces a new family of distributions based on the T-X framework by employing the Topp–Leone distribution as a generator. The resulting T-Topp−Leone{Y} family is developed, and three subclasses are obtained using the exponential, Weibull, and log-normal distributions. To increase modeling flexibility, the Lindley distribution is incorporated into the proposed framework. Several statistical properties of the proposed family are derived, and parameter estimation is carried out using the maximum likelihood method. A simulation study is conducted to examine the performance of the estimators under different sample sizes. The results indicate that the bias and root mean squared error decrease as the sample size increases, demonstrating satisfactory estimation performance. The usefulness of the proposed models is illustrated using two real datasets. Model performance is evaluated through the Kolmogorov–Smirnov statistic, Anderson–Darling statistic, log-likelihood, AIC, and BIC, and compared with several existing lifetime distributions. The results show that the proposed models provide competitive fits and accommodate a variety of distributional shapes. In particular, the L-TL{E} and L-TL{LN} models exhibit strong performance across the datasets considered. These findings demonstrate the potential of the proposed family for lifetime and reliability data analysis.