The last few days I am kind of confused about the concept behind a BRDF that uses a normalized Gaussian function to describe it's reflection behavior. More specifically, I am writing a hair shader using the Marschner hair model and in this model light is reflected in a lobe described by a Gaussian function. Since the standard deviation expressed in radians, is very close to zero, the normalized Gaussian function returns values larger than one for angles close to the expected value. When using this function as a BRDF, the reflection will be greater than one for some of the angles. This confuses me, since it does not make sense that for some angles the reflected light will be larger than the incoming light.
Now I have read that this normalized function is a PDF and that you have to integrate it to find the probabilities. But how would I use this normalized Gaussian function then to compute the amount of reflected radiance?