I've never tried to really model Improved aspect of the hawk mathematically. But I did build a simulator to simulate it and the results were pretty interesting. You can find the code for simulator here:
http://www.kotikone.fi/quenta/wow/HunterSimul.java
The rules I used in the simulator were following:
1. If aimed shot is not on cooldown then autoshot
2. If less than 3 autoshots are fired after last aimed shot then autoshot
3. If 3 or more autoshots fired and aimedshot cooldown gone, then aimedshot
Iaoth proc chance was calculated on every shot, and aimed shot casttime was modified with iaoth haste when it was on. That magic number 3 came from Lactoses tables in wow-europe.com, where it seems it's always the best bet. If your clipped shots are 2, then use full cycle and if your clipped shots are 3 or more, then clipped.
Simulate it 1 million times for every weaponspeed between 2.5 and 3.4 seconds with and without iaoth.
I had multishot simulated in there for a while. I dropped it out after it looked like it doesn't really make any difference. Just too much extra logic to take care of.
End result?
Time spent in iaoth proc was pretty consistent 23%.
For weapons with 3.0 - 3.4 speed the increase in both autoshots and aimedshots was always 1.7%.
2.8 - 2.9 speed weapons had 7-8% increase in autoshots and 1.7% in aimedshots.
2.6 - 2.7 speed weapons had 10-11% increase in autoshots and 1.7% in aimedshots.
I really felt like I've done an error somewhere, since that 1.7% is nowhere near the 4-5% people are claiming. :O
Tho it does make sense in some level. Since with 3.0 or slower weapons imp hawk does really nothing else than speed up your aimed shot casting. You won't shoot any more autoshots between aimed cooldowns there.
But when your weapon speed is 2.9 or faster, you suddenly can fit 1 more autoshot inside aimed shot cooldown.