why has to change to discretisized loss function?

[xfwu]

Really don't understand why it is needed to change logistic's pdf to cdf (which is sigmoid)... can't it be estimated directly by using logistic's pdf?
is it some stablization consideration?

Best

[raffy-bekhit]

cdf includes more information that can be used than the cdf.
So to compute the maximum liklihood estimation (MLE) all you have to do in the cdf is calculate the derivative about the wanted point ( let it be y) the higher the derivative ( slope ) the better.
the closer y to the mean and the smaller value of the standard deviation -> the higher the derivative is (higher porbability).
This all can be calculated by ( cdf(y+e) - cdf(y-e)) where e is a very small value.