A person with a psychopathic personality is one whose behavior is largely amoral and asocial, who is characterized by irresponsibility, lack of remorse or shame, perverse or impulsive behavior and other serious defects.  Dr. Hervey Cleckley describes in his book The Mask of Sanity, 16 characteristics of a psychopath:

Superficial charm and good intelligence
Delusions and other signs of irrational thinking
Absence of nervousness or neuroticism
Unreliability
Untruthfulness and insincerity
Lack of remorse or shame
Inadequately motivated antisocial behavior
Poor judgment and failure to learn by experience
Pathological egocentricity and incapacity for love
General poverty in major affective emotions
Specific loss of insight
Unresponsiveness in general interpersonal relations
Fantastic or uninviting behavior with alcoholic drinks
Suicide rarely carried out
Sex life impersonal, trivial or poorly integrated
Failure to follow any life plan

Psychotic Personality

The psychotic personality suffers from a psychosis which is a major mental disorder in which the personality is very seriously disorganized and contact with reality is usually impaired. Characteristics are:

Loner-type personality
Generally remains isolated or secluded
Uncomfortable around people
Lacks interpersonal skills
The person may also suffer from:
Delusions, Hallucinations, Disorganized speech,  and strange mannerisms
Incoherence, fragmented speech, inappropriate response