Billy Joel is actually very "shy" and "deeply introverted", according to his daughter Alexa Ray Joel

Alexa told New York Post column PageSix: "You know my father is really funny because he's he's like the most self-effacing person on the planet right?

"He never buys [into] his own hype.

"I'm like: 'You should be so proud of yourself!' He's like: 'Eh.' He's just not a typical, like narcissistic guy in the spotlight - he just does not buy into any of it -he's a true artist. He so deeply introverted, he's really actually a shy person."

Alexa went on to insist Billy is now "bored" of the hype around his new HBO documentary Billy Joel: And So It Goes, which details his rise to fame and the highs and lows of his music career.

She added: "He's like, well you know I'm kind of bored by it because it's a lot about me and I get sick of me ...

"He's so introspective, you know, so I think it'll hit him later. I think maybe in a few months from now [he'll] watch it and be like: 'Oh that's cool'."

The two-part documentary has won a slew of positive reviews since its release last month, and co-director Susan Lacy recently revealed she managed to get the famously private star to open up by explaining it wasn't a "drive-by portrait" project.

She told The Hollywood Reporter: "He actually said to me: 'It's not my film, it's yours. The only thing I ask is tell the truth. Just tell the truth.'

"And he came to the table with that, and I did about 10 very long interviews with him, and he delivered.

"I don't know that he was actually really ready at the beginning to tell his story, but he came to realize that we were making a very deep film, a very serious film, the one that was really going to explore his music and how it connected with his life ...

"It wasn't a fly-by-night, drive-by portrait, as many people do. He recognised that this was serious ... "