I think I saw percentages of Types and INFJ and INTJ were the rarest.
This is especially the case if you are a male INFJ or a female INTJ.
The cruel Irony? Im an INFJ, and my sister is an INTJ
Which brings me to a question: how is your (all of you) family divided up?
I'm highly suspicious of "they're the rarest" comments in descriptions. Even if it is true, it seems very unhelpful to state it. There is no point to it regarding how your mind operates.
Anyway.
Estimated types:
Younger brother: ESTP
Mother: ESFJ
Father: IxTJ
I get on with my brother and mother well.
I can share ideas with my father, but I can't really discuss them. It always ends up with him trying to show how right he is--without much factual backup--rather than exploring the topic further.
On the other hand, I can discuss things with my brother, but when it comes to a debate, my debate/persuasion skills are rather poor compared to him (actually, I'm fairly sure he could talk "Sneakers O'Toole"* into taking his sneakers off

).
I feel like I can talk about anything with my mother, and if I have a problem, she's usually one of the people I go to first because I know she'll help me feel like I'm not crazy in regards to what I'm feeling. If I need help with solving the problem, I seek out my brother/someone objective.
I definitely have never been made to be the "odd one out" in my family (eventhough I have alienated myself and made myself think I am sometimes), and I think it's because my mother has done her best to create an environment where it's okay to be who you are and you are never going to be expected to be someone else. This doesn't mean there aren't moments of awkwardness, though.
*
Family Guy Wiki said:
Sneakers O'Toole
A man who doesnt like to take his sneakers off. Two men approach him, yelling at him to take his sneakers off. He then jumps away, with the other man saying that they'll never catch him in the shoes they're wearing.
Regrettably Sneakers O'Toole escaped and has yet to be captured.