In arid and semi-arid regions, precipitation and seasonal streamflow are the two major sources of water for vegetation. The scarcity of these water sources has a detrimental effect on vegetation cover degradation. The purpose of this research is to study the effect of meteorological and hydrological droughts, and also their combined effects, on vegetation changes in seven coastal sub-basins in southern Iran (part of the Bandar-Sedij and Kol-Mehran catchment). To track meteorological and hydrological droughts, the Standardized Precipitation Index (SPI) and the Streamflow Drought Index (SDI) were used. The copula function and the entropy approach (which is developed in this research) were used to blend individual meteorological and hydrological drought indices, yielding hybrid indices called the Copula-based Drought Index and the Entropy-based Drought Index (EnDI). The single (i.e., SPI and SDI) and hybrid drought indices (CoDI and EnDI) were compared in terms of temporal behavior, drought severity and duration characteristics, drought frequency, and a bivariate analysis of the drought severity-duration return period. The results indicated that the rank correlation (\({r}_{s}\)) between SPI and SDI ranged between 0.327 and 0.726 in the studied sub-basins. However, the two hybrid indices CoDI and EnDI had extremely high correlations (\({r}_{s}\ge 0.9\)). Despite the fact that meteorological droughts benefited both hybrid drought indices more than hydrological droughts, the contribution of meteorological droughts to EnDI was greater than that of CoDI. Over the study region, CoDI reported droughts that were both longer and more severe than those recorded by EnDI. EnDI showed stronger associations with the Normalized Vegetation Difference Index (NDVI) in nearly all the sub-basins, possibly because precipitation has a greater effect on EnDI than it does on CoDI. EnDI was therefore recommended as a superior index for estimating vegetation droughts throughout the research region.