http://tvtropes.org/pmwiki/pmwiki.php/Main/InsaneEqualsViolent
What's more, the fictional psychotic will not only be invariably violent, he'll actually be more lethally effective than a sane person. Count on the villainous psychotic to be a nigh-unstoppable assassin who's mastered Offscreen Teleportation rather than, say, a poor deluded man uselessly arguing with or attacking his own hallucinations, or getting caught during his very first crime because he wasn't trying to escape.
In reality, people who have mental illnesses (not counting drug addiction) are statistically less likely to be violent than the average person; but when they are violent, it tends to be highly publicized. After all, if you're a journalist, why write about yet another murderer when you can write about a psychotic murderer? This creates horrible Unfortunate Implications as the public will instantly generalize anyone with a mental disorder as "a serial killer in-waiting" and ostracize the person. For someone with a mental illness involving depression, this can drive them over the edge and, occasionally, cause a Self Fulfilling Prophecy. This often deepens the social injustice against such persons, in that they are typically more vulnerable to such abuse, to due their infirmity and isolation, and are likewise acutely aware of such— thus creating a self-fulling prophecy in which the victim is blamed for "bringing it on themselves."