Water is important to live because of its impacts on food supply and the natural environment for all living things. Approximately 0.3 percent of water resources are usable in the world. Groundwater is the principal source of drinking water but the air, sea, land, rivers, lakes, ocean, and wells are also the essential sources of water. Many statistical models have been used to analyze the water data set so that to make predictions in a better way with limited resources of water. In this paper, a new approach is offered to model the data of water purification using vinyl chloride data. Various statistical properties of the proposed model have been derived. Maximum likelihood estimation is used to estimate the model parameters. Monte Carlo simulations are used to show the consistency of parameters. Using water purification using vinyl chloride, the suggested model application is studied and compared with that of other existing models such as EGF, GF, and F. The results showed that our model provides a much better fit while modeling this data set rather than EGF, GF, and F distributions.

Some characterizations and entropy measures of the Exponentiated Generalized Fréchet Geometric (EGFG) distribution are studied in this paper. Firstly, characterizations of the EGFG distribution based on five different approaches are discussed. The submodels for the EGFG distribution with their characterization expressions formed on the ratio of two truncated moments are also presented. Secondly, four different entropy measures are considered and expressed analytically via the incomplete gamma function. The behavior of all these entropy measures is discussed by performing a numerical study.