Another similar definition is deviation from socio-cultural norms, not statistical ones. In this definition, abnormality is when one violates behaviors that most consider proper. For example, not shaving, not going to church, and so on, would be abnormal. The difference between this definition and the previous one is that it is not the prevalence of the behavior that makes it normal, but rather the perception of propriety instead.
Other definitions are based on individuals instead of groups. For example, if a person feels uncomfortable in situations where others do not, then that person may be maladjusted. Similarly, a person may feel distress in situations where others do not. Or, a person may react in a less mature fashion than others do in particular situations. Edwin Arlington Robinson's poem "Richard Cory" exploits these individualistic kinds of definitions. In that poem, Richard Cory is cast as a man who has everything a person could possibly want. Yet, in the end, he commits suicide.
Another possible definition is simply being in trouble: trouble at home, work, school, or with the law, for example. When other people start to notice that you cannot adequately deal with your responsibilities, you may be in trouble. The commercials for private mental hospitals on TV are good examples. In one, a wife is calling her husband's boss because her husband is an alcoholic, and did not come to work after lunch, again. The message at the end is that maybe it is time that he, and she, do something about their trouble, namely, call that hospital.
The definitions above give you some idea of the possible range of abnormal behavior, yet none of them is entirely satisfactory. Also, you should not expect ever to find a completely satisfactory definition of abnormal behavior.