Extended odd Weibull–Lindley distribution

A novel extension of the Lindley and Weibull distributions is proposed in this article by combining the Lindley distribution with the extended odd Weibull family, termed the extended odd Weibull–Lindley (EOWL) distribution. The statistical properties of the EOWL distribution are derived, including a linear representation for its probability density function, moments, quantiles, and moment generation functions. Three parameter estimation methods (maximum likelihood, maximum spacing product, and least squares estimations) are explored. Monte Carlo simulations are conducted to evaluate the effectiveness of the estimator methods. Finally, in order to illustrate the flexibility and validity of the proposed distribution, three real datasets are employed. The results show that the EOWL distribution demonstrates a superior fitting performance compared to other established distributions.