[BUG] sigma_ behaving erratically

[henrydingliu]

Are you on the latest chainladder version?

• Yes, this bug occurs on the latest version.

Describe the bug in words

sigma_ can behave in unintuitive ways.

How can the bug be reproduced?

we can construct a hypothetical triangle where the dollars amounts are consistent YoY. this means that the ldf_ themselves don't diff a lot between simply average or volume weight average. however, the sigma_ show a large gap that i don't know how to explain.

data = {
    "valuation": [
        1981,1982,1983,1984,1985,
        1982,1983,1984,1985,
        1983,1984,1985,
        1984,1985,
        1985,
    ],
    "origin": [
        1981,1981,1981,1981,1981,
        1982,1982,1982,1982,
        1983,1983,1983,
        1984,1984,
        1985,
    ],
    "values": [
        1000,1385,1700,1905,2000,
        1000,1395,1700,1895,
        1000,1405,1700,
        1000,1415,
        1000,
    ],
}
tri = cl.Triangle(
    data,
    origin="origin",
    development="valuation",
    columns=["values"],
    cumulative=True,
)
print(cl.Development(average='simple').fit(tri).ldf_)
print(cl.Development(average='volume').fit(tri).ldf_)
print(cl.Development(average='simple').fit(tri).sigma_)
print(cl.Development(average='volume').fit(tri).sigma_)

       12-24    24-36     36-48     48-60
(All)    1.4  1.21868  1.117647  1.049869
       12-24     24-36     36-48     48-60
(All)    1.4  1.218638  1.117647  1.049869
         12-24     24-36     36-48     48-60
(All)  0.01291  0.008736  0.004159  0.002503
          12-24     24-36     36-48     48-60
(All)  0.408248  0.326286  0.171499  0.119197

What is the expected behavior?

The sigma_ of these two development estimators should be much closer when the triangle itself has stable volume over origin periods.