Is there a connection between anger and depression?
Freud first posed the connection between anger turned inwards and the onset of depression in his classic paper, "Mourning and Melancholia."
While many depressed people are self-critical, it is a stretch to say that they are basically angry at the outside world and just happen to be turning it in on themselves. Self-criticism is a symptom of depression, and we often see it alleviated by effective treatment.
Another approach is to look at the chemistry of aggression and depression. In both conditions, low activity of the neurotransmitter serotonin appears to play an important role. Some depressed people, in fact, can be quite aggressive, either showing irritability towards others, or in the worst case, violently harming themselves in suicide attempts.
Researchers suggest that low serotonin activity may be the culprit when suicide involves violent means.