Distribution of toxic players by rank?

Hi

I was discussing with some friends about distribution of toxic players. I remember Lyte saying that about 5% of League players are toxic, 1% being very toxic. But these numbers are for the total of players, while I know many people claiming that toxicity is much more common at low ranks (and I could understand why).

Is there anything official (an article, data of any kind, whatever...) that gives statistics of toxic players in relation to their rank? It would also be interesting to see if there is data about how common toxicity is in the various game modes (ranked vs normal, coop vs pvp vs custom vs team, aram vs dominion...)