add_asym is a Python code for adding numbers with asymmetric uncertainties. Basically just a numerical implementation of the statistical methods discussed in Barlow (2003, arXiv:0306138), the code was developed as a part of the work leading to the paper Lyman α-emitting galaxies in the epoch of reionization.
If you use the code for scientific use, I'd be happy if you could cite Laursen et al. (2019, A&A, 627, 84), where the code is described, tested, and applied.
I will write a better description in the bottom of this document soon at some point, but really all you need is the file add_asym.py, in which the docstring describes how — and in particular why — to use the code.
To add the following numbers
define arrays/lists containing the central values, lower errors, and upper errors, respectively, and call add_asym with these arrays, using either a linear transformation (order=1) or a quadratic transformation (order=2):
>>> from add_asym import add_asym
>>> x0 = [5,3,4] # Central values
>>> s1 = [2,3,3] # Lower errors (do not include the minus)
>>> s2 = [1,1,2] # Upper errors
>>> add_asym(x0,s1,s2,order=1) # Add numbers (using a linear transformation)
array([10.92030132, 4.23748786, 2.94389109])The output is the central value, the lower error, and the upper error, respectively. That is, the result would be written . Using
order=2 yields a slightly different result, namely . None of these can be said to be more correct than the other when the full PDFs are not known. But in general, both results will be a better approximation than the standard, but wrong, way of adding upper and lower errors in quadrature separately, i.e.
This result can be acheived setting order=0, but will output a warning:
>>> add_asym(x0,s1,s2,order=0)
This is WRONG! Mark my words, it is WROOOOOONG!!!
array([12. , 4.69041576, 2.44948974])