This paper introduces a new one-parameter distribution derived from the Lindley distribution, called the modified Lindley distribution. Its main feature is to operate a simple trade-off between the exponential and Lindley distributions, offering an interesting alternative to these two well-established distributions. We study the main properties of the proposed distribution, with a special emphasis on its moments, reliability parameter and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments and maximum likelihood methods. Three applications reveal that the new model has the ability to fit well practical data sets.

The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.

This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as quantitative researchers for their further collaborative learning with an analytical base.

To model data in angular form, circular distributions are the most appropriate mathematical tools. In this paper, we introduce a new one-parameter circular distribution based on the wrapping method, called the wrapped modified Lindley distribution. Characteristic function and fundamental properties of this distribution are described. Method of maximum likelihood estimation is used for the estimation of the parameter. The proposed model is applied to two real-life datasets, and its performance is compared with that of the wrapped Lindley, wrapped exponential and transmuted wrapped exponential models.