We don't know what you mean by "normal probablity density function or normal density function". What would the distribution be of ?
I don't know what the "standard edge based algorithm" is. They all use different algorithms. The "true" location of an edge is often a judgment call, so who's to say which on is "right"? What counts is if you can get your task done after using one of them.
So whatyou do is to just try them all, tweaking each until you achieve the "best" edges then see if you can complete the rest of the task. If you have ground truth then you can see which one did best. You can use an ROC curve perhaps. Maybe one didn't give closed curves and you needed closed curves to get solid blobs. So that one would not find as many as some other edge algorithm. You can compare them that way.
