What is the physical or statistical meaning of the following integral
where is a Gaussian in describing the transition frequency fluctuation in a gaseous system (assume two-level and inhomogeneous) .
, where is the peak frequency and the running frequency.
I understand that the integral finds a point for which the area under the curve (the Gaussian) between 0 to a and a to are equal.
But is there a statistical meaning to this integral? Does it find something like the most-probable value ? But the most probable value should be in my understanding! So what does the point tell us?
I will be grateful if somebody can explain this and/or direct me to a reference.