Describing NDVI data from the GOLL-I regression

The study of vegetation indices is of crucial importance for economic development. Among them, the normalized difference vegetation index (NDVI) has occupied a promising position due to its easy interpretability of real phenomena. In this paper, we propose a regression model in which the response variable is linked to the NDVI support. To this end, a new mean-based reparametrized distribution is introduced, and some of its mathematical properties are derived, such as variance, kurtosis, skewness, and Shannon entropy. We discuss how to obtain maximum likelihood estimators (MLEs) for the regression parameters and matrix-based closed-form expressions for the score function and the Fisher information matrix. In particular, we show that MLEs can be formulated via the scoring Fisher method using simple interactive equations. To quantify the behaviour of the MLEs, we perform a Monte Carlo simulation study. Finally, we apply our model to describe how NDVI data are related to the Enhanced Vegetation Index (EVI), using information from the state of Pernambuco in Brazil. The results show that the relationship (NDVI, EVI) is meaningful, and our proposal outperforms the classical linear and beta models used in practice.