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.

Modeling bounded response variables is an important problem in computational statistics, especially in applications involving skewed, heavy-tailed data. In such cases, the modal regression is a robust alternative to traditional mean-based modeling approaches. In this study, a new bounded distribution, called the extended Bradford distribution, is proposed as a flexible extension of the classical Bradford distribution. By incorporating an additional shape parameter, the corresponding model can capture various shape structures, such as left and right skewness, increasing, and bathtub hazard shapes. The new distribution provides an explicit expression for the mode, making it suitable for modal regression. Based on this, a parametric modal regression model is developed, and parameter estimation is performed via the maximum likelihood method. The behavior of the estimators is investigated through comprehensive simulation studies. The practical usefulness of the proposed model is illustrated through applications, where the proposed model provides an improved fit compared to several competing models. In addition, an interactive R Shiny application is developed to facilitate the implementation, computation, and visualization of the model.

Count regression models are important statistical tools to model the discrete dependent variable with known covariates. When the dependent variable exhibits over-dispersion and inflation at zero point, the zero-inflated negative-binomial regression model is used. The presented paper offers a new model as an alternative to the zero-inflated negative-binomial regression model. To do this, Poisson generalized-Lindley distribution is re-parametrized and its parameter estimation problem is discussed via maximum likelihood estimation method. The proposed model is called as zero-inflated Poisson generalized Lindley regression model. The results regarding the efficiency of parameter estimation of the proposed model are evaluated with two simulation studies. To evaluate the success of the proposed model in the case of zero inflation, two datasets are analyzed. According to the results obtained, the proposed model gives better results than the negative-binomial regression model both in case of over-dispersion and in the case of zero inflation.