Two parameter log-Lindley distribution with LTPL web-tool

This paper introduces the two-parameter log-Lindley distribution. It can be presented as a new flexible distribution supported on the interval $(0,1)$, which includes the famous log-Lindley distribution as a sub-distribution. Its important probabilistic properties are discussed. On the applied side, a statistical focus was placed on the corresponding model. Three methods were used for the parameter estimation and the effectiveness of these methods was evaluated by a simulation study. The superiority of the proposed distribution over other distributions was demonstrated with three applications on real data sets. A significant aspect of the study is the development of an associated web tool. The LTPL web tool was designed to enable users to utilize the newly developed probability distribution without requiring any programming expertise.