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This study investigates the changes in the drought frequency in 2070–2099 relative to 1970–1999, due to the mean and shape changes of the probability density function (PDF) of the self-calibrated Palmer Drought Severity Index (PDSI), using CMIP5 multi-model historical simulations and projections under the RCP4.5 scenario. For severe droughts defined with PDSIs less than the 10th percentile, it is shown that over 41% of the global land, the increase in the severe drought frequency due to the shape change exacerbates the increase due to the mean change. Over 28% of the global land, the decrease in the drought frequency due to the shape change partially offsets the increase due to the mean change. Over 31% of the global land, the drought frequency increases due to the shape changes, but decreases due to the mean changes. The severe drought frequency due to both PDSI PDF mean and shape changes increases over almost the entire global land. We show that the PDSI standard deviation change is mainly determined by the mean precipitation change, while the PDSI mean change is determined by both mean precipitation and potential evapotranspiration changes. In particular, the PDSI standard deviation increases with the increase in mean precipitation which broadens the PDSI PDF, and thus enhances the severe drought frequency, and vice versa. On the other hand, the PDSI mean decreases with the decrease (increase) in mean precipitation (mean potential evapotranspiration). The difference in the attribution of drought frequency changes to the mean and shape changes over different regions can thus be largely explained by the mean precipitation and potential evapotranspiration changes. We also examine the moderate droughts defined with PDSIs between 10th and 20th percentiles in this study. For the moderate drought frequency, the spatial pattern of its changes due to the PDSI mean changes is similar to that of severe drought but with much smaller magnitudes, while its change in the spatial pattern due to the shape changes differs from severe drought with no significant changes. The moderate drought frequency due to both PDSI PDF mean and shape changes increases over 71% of the global land but decreases over 29% of the land. more...