Cases in which a juvenile is accused of killing both parents are exceedingly rare. Dr. Kathleen Heide, a professor of criminology at the University of South Florida who has studied parricide for 30 years, said in a phone interview Tuesday that cases such as the Winthrop killings, in which a juvenile is accused of slaying both parents, represent less than 10 percent of the roughly 250 murders of parents by their offspring reported annually in the nation. Emphasizing that she has no specific information about the Winthrop murders, Heide said that in most parent-homicide cases, the offenders fall into four categories: the severely abused child, the severely mentally ill child, the dangerously anti-social child and the enraged child.