The commonly used precipitation-based drought indices typically rely on probability distribution functions that can be suitable when the data exhibit minimal discrepancies. However, in arid and semi-arid regions, the precipitation data often display significant discrepancies due to highly irregular rainfall patterns. Consequently, imposing any probability distributions on the data for drought analysis in such regions may not be effective. To address this issue, this study employs a novel drought index called the Discrepancy Precipitation Index (DPI), specifically designed for arid regions. Unlike traditional methods, the DPI does not impose a probability distribution on the precipitation data; instead, it relies on the discrepancy between the data and the mean value. Drought severity classifications (i.e., Drought-I, Drought-II, and Drought-III) are proposed based on the DPI values. The DPI is used to characterize and assess the meteorological drought years based on annual and monsoonal precipitation over nineteen districts in Western Rajasthan, India, during 1901–2019. Additionally, a novel statistic called Discrepancy Measure (DM) is employed to assess the degree of discrepancy in the precipitation climatology of the districts for annual and monsoon precipitation time series. Based on annual precipitation, Jaisalmer district exhibited the highest number of historical drought years (35), whereas three districts, i.e., Jhunjhunu, Dausa, and Bhilwara exhibited the lowest number of drought years (11). Similarly, based on monsoon precipitation, Jaisalmer and Bhilwara encountered the highest (34) and the lowest (11) number of drought years, respectively. The return period of Drought-II is lower for monsoon precipitation-based DPI as compared to that of the annual precipitation-based DPI for all the districts. The DM and DPI-based total number of droughts are found to be strongly correlated for both annual and monsoon precipitation. The DM value is highest for Jaisalmer and lowest for Bhilwara district. The findings reveal DPI as an efficient tool for assessing drought years, particularly in arid climatic conditions. Moreover, as the DM value increases for a precipitation series, the DPI becomes more effective in capturing drought events.