Do active speakers have high THD amplifiers?

No, THD is THD, all amplifiers today have lower THD than the speakers they drive. The biggest improvement comes in the form of intermodulation distortion (IMD) which is virtually non-existent with active speakers. Intermodulation distortion is what your ears dislike the most, some people may call it sterile or mechanical, I call it accurate. I prefer to do it with my own amplifier choices using a DSP or electronic crossover. This gives you so many more choices than an active speaker where the speaker manufacture get to decide what amps, crossover points and slopes to use.  The biggest improvement will come in the way of much more defined midrange and high frequencies. I've been bi-amping and tri-amping for 42 years. Will only go back to passives when I need to downsize to move into a retirement community.

yes, very high thd... and imd... or else they wouldn't sound good...

just kidding

use your common sense... 

 Their only significant problem is a rather noisy fan..

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Behringer NU12000 are the same way.. I have a few (:-)). I can find them for around 375-500. New or refurbished. They have 3 fans. I disconnect 2 of the 3 and put the third over the PS on a mini toggle.

Late night listening I flip the switch off. I have forgot several times and finally left it off. That was 2.5 years ago.. That is a bullet proof class d at 27 lbs.

Regards

@ashoka --

...  My question is which audiophile active speakers have better amplifier specifications.

Active, bundled speakers are often claimed to have "matched" amp-to-driver implementation, but much of this is a gimmick, I find. With active configuration the amp matters less, or the same amp will be given much better conditions to perform at its fuller potential not seeing into a passive cross-over, and so the matched nature is really less important vs. matching amps to passive speakers. Not that matching amps in active configs can't bring advantages, but it's been a cloak for some time now that some active speaker manufacturers have worn to make their endeavors appear esoteric. Give me a break. 

In any case active means better driver control, and it translates - in the combinations I've heard - into less smear, better resolution and transparency. Passive by comparison sounds thicker, duller, more restrained and less immediate, but to other ears that's likely warmer, fuller and more pleasing/laid-back.

Most audiophiles (like in >99%) have been accustomed to the sound of passive speakers for decades - typically via hideously insensitive, smaller speakers - but passive speakers qua passive speakers as such have a rather easily discernible character compared not least to larger, more sensitive and active speakers, and that's something that most may likely never experience or acknowledge as a negative because by and large it's the same (passive) meal they've been served for years. As long as people are happy, to each their own and all that jazz, but active for just named reasons haven't been given due credit where it very much should. 

Good amplifiers tend to be the norm rather than the opposite. If you are buying active speakers from a reputable manufacturer, I'm sure it's a well measuring amplifier.  You should listen to the combo and go by that more than specs.