Drought is natural phenomenon. drought is the deficit that results where soil moisture is insufficient to meet the demands of potential evaporation. It can be classified as a (1) permanent drought associated with arid climate, (2) seasonal drought , which occurs in climates with distinct annual period of dry weather,and (3) drought due to precipitation variability.
normally the drought indicators are depends upon the above conditions & classification..........
We can, however, identify various indicators of drought, such as rainfall, snowpack, streamflow, and more, and track these indicators to monitor drought. ... A drought index value is typically a single number, which is interpreted on a scale of abnormally wet, average, and abnormally dry
You can specifically look the works of Vimal Mishra (IIT Gandhinagar).
Article Trends and variability of droughts over the Indian monsoon region
Please look at this article where you can find several drought index {e.g. standard precipitation index (SPI), standardized precipitation-evapotranspiration index (SPEI), Gaussian mixture model-based drought index (GMM-DI), and hidden Markov model-based drought index (HMM-DI)}.