Environmental Data Analysis with a Versatile Model on Time Scales

We proposed a discrete Lindley distribution with a nabla structure, taking into account the nature of the underlying environmental data. To understand the behavior of the proposed distribution and how it can be effectively used in the considered scenario, some its mathematical properties are studied. These properties include generation functions, moments, index of dispersion, order statistics, and asymptotic distribution of the extremes. We have also studied its application and found that the proposed statistical model is one of the better choices in modeling the environmental indicators, such as concentration of carbon monoxide, nitrogen oxide, and number of precipitation days.