Loglikelihood function for Gaussian exponential family distribution.
Parameters: | endog : array-like
mu : array-like
scale : float, optional
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Returns: | llf : float
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Notes
If the link is the identity link function then the loglikelihood function is the same as the classical OLS model. llf = -(nobs/2)*(log(SSR) + (1 + log(2*pi/nobs))) where SSR = sum((endog-link^(-1)(mu))**2)
If the links is not the identity link then the loglikelihood function is defined as llf = sum((endog`*`mu-mu`**2/2)/`scale - endog`**2/(2*`scale) - (1/2.)*log(2*pi*`scale`))