Is there any index that measures similarity between 2 gaussian distributions of 1-D data (may have slightly different number of points) considering their mean shift, variance shift, difference in shapes(like one is symmetric and the other is skewed) etc. and gives similarity between [0,1]?
I am using Hedges' index for the same but it does not give a similarity index between 0 and 1. It can be greater than 1 as well, so it is difficult to interpret it.
Also, no pattern of the data is known beforehand, if it helps in any way for the answer.