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Caitlyn Jenner has explained why, unlike any other member of her family, she agreed to participate in the documentary series House of Kardashian, exploring the singular rise to riches of its members.

Jenner, who is the father of Kylie and Kendall Jenner, and the step-father of Kim, Kourtney and Khloe Kardashian, told The Times of London she wanted to make sure the family was represented in the right way.

She said:

“It’s very difficult when you’re in public life and in the media, especially the Kardashians… Sometimes it’s just very disappointing to see how they’re represented. And when they approached me about doing this show, once I thought about it, I thought, ‘You know what? I want to get involved. I want to do my best to be very positive and really represent the family and the kids in a positive way.’”

No other family member appears on camera, and nor has Jenner spoken to them about the series, she said:

“I really haven’t talked with them about it. I’m kind of doing this on my own. I’ve been in the media for a long time. I know how the game is played.”

The documentary series, which premieres on Sunday, explores the evolution of the Kardashian clan from the 1970s when Jenner was an American sporting superstar after winning decathlon Olympic gold, through the 1980s when Kris was the wife of lawyer Robert Kardashian, traumatised when he represented his friend OJ Simpson in the trial of the murder of her good friend Nicole Simpson, and into the noughties, when the combination of a sex tape, a reality TV series and the advent of social media turned the whole family into household names and a collection of billion-dollar brands.

Caitlyn had played a supporting role in the reality series, with cameras focused mainly on his wife and step-daughters. That changed in April 2015 when Caitlyn came out on television as a trans woman, followed up by a Vanity Fair cover shoot and a two-part special About Bruce, in which she spoke to her family about her transition.