New Modified Univariate Lindley Distribution: Statistical Properties, Estimation, and Applications

This article centers on the exploration of a new univariate probability distribution. A novel distribution has been formulated using the power transformation technique, termed the new modified univariate Lindley distribution. This model exhibits diverse hazard functions, including J-shaped, reverse-J-shaped, and monotonically increasing pat-terns. The study examines the fundamental statistical characteristics of this recently introduced distribution, including moments, incomplete moments, hazard rate, mean residual life function, quantile function, skewness, and kurtosis. Estimation of its parameters is conducted through the maximum likelihood estimation method. The precision of this parameter estimation process is verified through Monte Carlo simulation experiments. To illustrate the practical utility of the proposed distribution, two sets of real-world data are employed. The performance of the suggested distribution model is assessed using various model selection criteria and goodness-of-fit test statistics. Empirical findings from these evaluations provide substantial evidence that the proposed model surpasses other existing models.