Parrots never scream for no reason..
What we call a "scream" is a way of communication for the parrot. The problem is that we do not speak their language, which is what brings them to talk (scream)repeatedly and increasingly loudly so as to be understood. The same is true of humans: when someone does not understand us, we tend to speak louder and use different tones to make the other understand.
Parrots always vocalize in the morning when they wake up to greet the new day and at night to signal their position in the forest to other birds. They do the same in our households as it is written in their genes.
Other vocal manifestations are used to communicate with humans: the parrot is a living being which needs to express its fear, its joy, its needs and its desire to interact with the family. Therefore a parrot that screams, is a parrot which speaks its language, not ours. Hence, the troubles of understanding between man and bird. This is similar to two people who speak different languages, try to talk to each other: the less one of them understands, the more the other gets frustrated. The same is true of his counterpart.
A human baby that cries does not cry to anger his parents: it is its only way of expressing its discomfort, its fear, etc. Parents eventually learn to recognize the nuances in the cries and the different tones.
The same is true of parrots: to understand them, one must observe the current situation, the bird's body language, the time of the screaming as well as its intensity until one may eventually understand the message.
It is also important to remember that ambient noise such as television or radio sets playing loudly, barking dogs, childrens' cries all constitute auditive stimuli which may cause the bird to add its voice to the racket. If you want a calm bird, make sure that it is in a calm environment.