The Boogeyman English Movie

A psychiatrist, where a man named Lester Billings talks to the doctor about the "murders" of his three young children, describing the events of the past several years. His first two children died mysteriously of apparently unrelated causes (diagnosed as crib death and convulsions, respectively) when left alone in their bedrooms. The only commonalities were that the children cried "Boogeyman!" before being left alone, and the closet door ajar after discovering their corpses, even though Billings is certain the door was shut.