It is possible to train your bird to scream by your own misinterpretations of bird behavior. Alexandrines - noisy at times but usually only twice per day for a short period of time. Amazons - can be noisy but are also very entertaining and chatty .They usually love to vocalize in general. They have a very sharp loud cry, but again rarely use it constantly. If you have a Hawkhead, you will have this cry in your life.
Many pet owners find it is well worth it for their many wonderful traits.
Most smaller Ringnecks again have the capacity to be loud but for the most part are not. Eclectus parrots are also usually quiet but when they do squawk, you really know about it. Lovebirds, Cockatiels, Quakers, Budgies, Parrotlets, are usually considered moderate in noise level. They love to whistle, sing, and copy every noise they hear, such as water, phones, etc. Few people have any issue with their African Grey's noise level.