Statistics to characterize time-domain envelope of acoustic signal
An ADSR has exactly five parameters, and you need these five to characterize it - every set of parameters yields a different envelope.
And frankly, the ADSR envelope is pretty easy to visualize, and to understand:
So, calculate the envelope of your signal, find the

peak amplitude,
the time it takes to reach that peak
the plateau level
the time it takes to reach that plateau from the peak, and
the time it takes for the envelop to decay after leaving the plateau.

These are your five degrees of freedom, and they can be quite directly read from a slightly averaged envelope.