A novel flexible model: The Sine Topp Leone length-biased truncated lomax distribution

Abstract

This study presents a new extension of the length-biased truncated Lomax distribution by incorporating the sine Topp-Leone family, resulting in a flexible model called the sine Topp-Leone length-biased truncated Lomax distribution. The proposed distribution demonstrates remarkable adaptability in modeling data with increasing hazard rates. Key statistical and reliability properties of the new model are thoroughly examined, including the survival function, hazard rate, reversed hazard rate, quantile function, moments, incomplete moments, and Renyi and Tsallis entropy measures. Parameter estimation is conducted using both classical and Bayesian methods, considering symmetric and asymmetric loss functions. Due to the computational challenges of Bayesian estimation, Markov Chain Monte Carlo techniques with independent gamma priors are employed. Simulation studies confirm the consistency of the proposed estimators, showing improved accuracy with increasing sample size, with Bayesan estimates provide lower absolute biases and mean squared errors. Finally, applications to two real datasets demonstrate the superior flexibility and effectiveness of the proposed distribution compared to existing alternatives.