The Anscombe residuals
Parameters: | Y : array-like
mu : array-like
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Returns: | resid_anscombe : array
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Notes
sqrt(n)*(cox_snell(Y)-cox_snell(mu))/(mu**(1/6.)*(1-mu)**(1/6.))
where cox_snell is defined as cox_snell(x) = betainc(2/3., 2/3., x)*betainc(2/3.,2/3.) where betainc is the incomplete beta function
The name ‘cox_snell’ is idiosyncratic and is simply used for convenience following the approach suggested in Cox and Snell (1968). Further note that cox_snell(x) = x**(2/3.)/(2/3.)*hyp2f1(2/3.,1/3.,5/3.,x) where hyp2f1 is the hypergeometric 2f1 function. The Anscombe residuals are sometimes defined in the literature using the hyp2f1 formulation. Both betainc and hyp2f1 can be found in scipy.
References