ENH: (theoretical) noncentrality parameter implied by model, data generating process

[josef-pkt]

I'm using now Monte Carlo simulations to check how good hypothesis tests are.

AFAIK, we don't have anything to compute the theoretical noncentrality parameter for a parametrically specified model DGP used in simulations.

example

The return of Hosmer-Lemeshow type test for poisson includes several estimates of nc.
Test method delegates to statsmodels.stats.diagnostic_gen.test_chisquare_binning

Why is nc_umvue negative and much smaller than the other estimates?
I guess the theoretical nc=0 in this simulations which is under the null of correct specification.

noncentrality = <class 'statsmodels.tools.testing.Holder'>
    nc = 0.0
    confint = array([1.0000000000000e-100, 8.0294528361405e+000])
    nc_umvue = -1.8074724688857908
    nc_lzd = 0.5320879218523682
    nc_krs = 0.9121507231754883
    nc_median = 1e-100
    name = 'Noncentrality for chisquare-distributed random variable'