Summation of uncertainty intervals I have the following data based on the 6 independent regions that make up the world. I want to compile them to find a global estimate. I can add best estimates from each region to give the best estimate for the the world. I am not sure how to deal with the uncertainty intervals as I feel adding the low and high estimates does not seem correct




Region
Best Estimate
Low
High




African Region
379
321
441


Region of the Americas
19
18
20


Eastern Mediterranean Region
80
68
92


European Region
21
20
22


South-East Asia Region
698
650
747


Western Pacific Region
87
80
93




Ideally you'd have the raw data concatenate everything and with that you can make the uncertainty intervals. But if you only have this data, you could make assumption about the shape of distributions and simulate the result. For example assuming everthing is uniform:
import numpy as np
import pandas as pd

sim = []
for n in range(int(1e4)):
    africa = np.random.uniform(321, 421)
    americas = np.random.uniform(18, 20)
    medi = np.random.uniform(68, 92)
    europe = np.random.uniform(20, 22)
    sasia = np.random.uniform(650, 747)
    wpacific = np.random.uniform(80, 93)
    estimate = np.mean([africa, americas, medi, europe, sasia,wpacific])
    print(estimate)
    sim.append(estimate)


And with that is possible to estimate the intervals, and you could make this better weighting by the populations.
