NEW YORK (REUTERS) - California rappers NWA finally took their place in the Rock and Roll Hall of Fame on Friday, jubilant about their transformation from one of the most hated bands in America to music's mainstream.

British metal band Deep Purple, soft rock-pop group Chicago, singer Steve Miller, and 1970s rock band Cheap Trick rounded out the 2016 inductees, who were chosen by fans and more than 800 voters of the Rock Hall, housed in an IM Pei-designed edifice on the of Lake Erie in Cleveland, Ohio.

With Deep Purple, all three bands considered the trinity of British hard rock in the 1970s are in the Hall of Fame after Led Zeppelin and Black Sabbath. The band's current line-up, led by Ian Gillan, played hits including Highway Star, Hush and Smoke on the Water, whose bluesy but heavy opening is among the most famous in rock.

The group was joined by the tearful widow of Jon Lord, its energetic keyboardist who died in 2012, but not guitarist Ritchie Blackmore, who wrote the legendary Smoke on the Water riff and said the current band had made him unwelcome.

Drummer Ian Paice described Blackmore as a "singular animal", saying he might have turned up at the last minute. David Coverdale, a former Deep Purple singer who went on to lead Whitesnake, said he had emailed Blackmore several days ago in a last-ditch attempt to persuade him to come.

After Lord's death, "we buried the hatchet of 30 years of inflammatory oratory, so it's a big disappointment to me he wasn't there today", Coverdale told reporters.

Deep Purple were introduced by Metallica drummer Lars Ulrich, who said his life was transformed by seeing the hard rockers play his native Copenhagen when he was nine.

Donning a blazer in the colour of the band's name, Ulrich said Deep Purple both played "with raw intensity" as if by themselves yet "at the same time projected a thousand-yard deep stare into the bowels of the arena."

Chicago, which fused jazz and rock, performed their upbeat hit 25 or 6 to 4, but left out one of their best-known songs, the 1976 romantic ballad If You Leave Me Now.

NWA, formed in the 1980s in the troubled Compton neighbourhood of Los Angeles and enjoying new fame through the 2015 biopic Straight Outta Compton, were only the fifth hip hop act ever to be voted into the Hall of Fame. They had been nominated three times before.

The group made waves for their often inflammatory songs that reflected the violence, crime and anti-police sentiments of their neighbourhood, but went on to sell more than 100 million records.

Founding member Ice Cube said the group had earned their place in the Hall of Fame, just as the pioneers of jazz, blues, punk, rock and pop before them.

"We have come a long way from being so hated in the industry to making it to the Rock and Roll Hall of Fame," Ice Cube said."Are we rock and roll? You're (expletive) right we're rock and roll. Rock and roll is not conforming to the people who came before you, but creating your own path in music and in life."

NWA celebrated with Dr Dre taking a selfie on stage of the group.

Artists are eligible for inclusion 25 years after the release of their first recording.

Miller, who moved from blues to pop and back again to produce 1970s hits such as The Joker and Fly Like an Eagle lashed out backstage at the induction process.

He criticised restrictions over music and video licensing for the show and complained about being offered only two tickets for family and friends for the ceremony.

"This came so close to not happening," Miller said of his appearance at Friday's ceremony. "They make it so unpleasant."

Miller, born in Wisconsin where he learned guitar under the legendary Les Paul, emerged in the cultural mix of 1960s San Francisco as he blended jazz and blues with roots Americana. He still plays regularly at age 72 and guides the musical instrument collection at the Metropolitan Museum of Art in New York.

Chicago, who adapted the jazz of the band's namesake town to become soft- rock giants, brought out their celebrated horn section but played without former singer Peter Cetera, who also blamed organisers.

But Cheap Trick, the hard-working heartland rockers who became a surprise sensation in Japan, reunited on stage with drummer Bun E Carlos who only a few years ago was suing his bandmates.

"Who knew that 'I want you to want me' would become such a defining phrase for a rock band from Rockford, Illinois?" singer Robin Zander said of Cheap Trick's famous song. "Seems like such a stupid phrase. But it works, I guess."

The ceremony will be broadcast exclusively on HBO on April 30.