PDF normalization. about asymmetric_uncertainty

[cgobat]

I just checked the following:

from scipy.integrate import quad # function-based numeric integration/quadrature utility

p = a_u(200,10,15) # test value

integral, abserr = quad(p.pdf, p.value-(p.minus*6), p.value+(p.plus*6)) # arguments are (func, a, b)

print(integral) # outputs 0.9999999980336641

This seems like it's working as expected. Similarly, we could do

from scipy.integrate import trapezoid # array-based numeric integration utility

datap = a_u(200,10,15)
num_sigma = 5
discretization = 500
neg_x = np.linspace(datap.value-(num_sigma*datap.minus),datap.value,discretization)
pos_x = np.linspace(datap.value,datap.value+(num_sigma*datap.plus),discretization) # I changed this line relative to your example from datap.minus to datap.plus
x_arr = np.array(list(neg_x)+list(pos_x))

pdf = np.piecewise(x_arr, [x_arr<datap.value, x_arr>=datap.value],
                   [lambda y : np.sqrt(2)/np.sqrt(np.pi)/(datap.plus+datap.minus) * np.exp(-1*(y-datap.value)**2 / (2*datap.minus**2)),
                    lambda y : np.sqrt(2)/np.sqrt(np.pi)/(datap.plus+datap.minus) * np.exp(-1*(y-datap.value)**2 / (2*datap.plus**2))] )

integral = trapezoid(y=pdf, x=x_arr)

print(integral) # outputs 0.9999999980259466

Upon confirming that it seems to be doing the right thing, I realized the issue: in your second-to-last line, you divide by discretization to compute delta. The evaluation of the PDF uses a total of 2*discretization points, since there are discretization points both to the left and to the right of the nominal value. So there's the mystery factor of 2!