This is the second ponderous analysis of vaccine distribution data I've seen that misses the obvious explanation - most vaccines were distributed at the time of excess supply and low demand. At that time, the distribution was demand driven. https://twitter.com/SharadRaghavan/status/1387368798290776074

i.e. when a state was close to exhausting its stock, it asked for more, the Union government sent more. (This was explained by @Dev_Fadnavis in a thread) So the best explanatory variable for how much a state got is how effectively the state vaccinated

Of course, this explanation won't hold good in a supply constrained situation, but it is a reasonable explanation for the vaccines that were distributed so far. It is interesting that people are missing the obvious explanation