Not much is known about Tyrone. Due to his personality, it is more than possible that he grew up depressed and bitterly. It can be implied by his appearance, that he is Abraham Simpson's second oldest brother, after Great-Uncle Hubert.
At some point in his life, he moved to Dayton in Ohio. While living here, he presumably married and had Francine (formerly known as Frank) and an unnamed Simpson.
Marge tells Bart and Lisa they are going to Dayton Ohio for their great uncle Tyrone's birthday.
Lisa says when they were singing happy birthday to him last year he said "Why won't I die?". The kids decide not to go and stay home with Grandpa. Homer and Marge get on a different flight at the airport and don't go to see Tyrone.