Yes. No serious historian believes that Tyrion Lannister didn't kill his father. First, he escaped shortly after the death of Tywin. Second, though denied at the time by House Lannister, it has been confirmed that a dead whore called Shae, known to be Tyrion's lover was found dead in Tywin's bed, strangled to death. It is very possible that Tyrion went to confront his father, found Shae in his father's bed and ended up murdering both in a jealous rage. The smoking gun in this case is that Tyrion Lannister was often known to say that "he had slain both his parents." With this evidence and testimony, it is basically impossible to think that Tyrion didn't kill Tywin. Whether Tyrion was justified is a true matter of debate in my opinion.