Penso che qualcosa del genere potrebbe essere la soluzione in MATLAB:
[overlap] = calc_overlap_twonormal(2,2,0,1,-20,20,0.01)
% numerical integral of the overlapping area of two normal distributions:
% s1,s2...sigma of the normal distributions 1 and 2
% mu1,mu2...center of the normal distributions 1 and 2
% xstart,xend,xinterval...defines start, end and interval width
% example: [overlap] = calc_overlap_twonormal(2,2,0,1,-10,10,0.01)
function [overlap2] = calc_overlap_twonormal(s1,s2,mu1,mu2,xstart,xend,xinterval)
clf
x_range=xstart:xinterval:xend;
plot(x_range,[normpdf(x_range,mu1,s1)' normpdf(x_range,mu2,s2)']);
hold on
area(x_range,min([normpdf(x_range,mu1,s1)' normpdf(x_range,mu2,s2)']'));
overlap=cumtrapz(x_range,min([normpdf(x_range,mu1,s1)' normpdf(x_range,mu2,s2)']'));
overlap2 = overlap(end);
[overlap] = calc_overlap_twonormal(2,2,0,1,-10,10,0.01)
Almeno potrei riprodurre il valore 0.8026 riportato di seguito in Fig.1 in questo pdf .
Devi solo adattare i valori di inizio e fine e intervallo per essere precisi in quanto questa è solo una soluzione numerica.