A turbine engine will try to spin at a certain speed in each power setting and if there is a loss of power somewhere (bleed leak for example) you will notice an increase in the EGT because it puts on more fuel to produce the same amount of power, however thats not the case in the humidity effect It's as I said before, Humidity does affect the performance but the influence is negligible because of the way the combustion chambers are designed and the fact that most of the air goes through the bypass.