Deviance of the unifed distribution
unifed.deviance(y.v, mu.v, wt = 1, ...)unifed.unit.deviance(y, mu, tol = 1e-07, maxit = 50)
A numeric vector with values between 0 and 1
A numeric vector with values between 0 and 1
(default value: 1) The weight vector. It contains the weight of each observation. It must contain positive integers only.
Additional parameters of unifed.kappa.prime.inverse.one
A vector with values between 0 and 1.
A vector with values between 0 and 1.
Tolerance level for the Newton-Raphson algorithm for computing the inverse of the derivative of the cumulant generator of the family.
Maximum number of iterations for the Newton-Raphson algorithm for computing the inverse of the derivative of the cumulant generator of the family.
unifed.deviance returns the deviance of a GLM with a
unifed response distribution. This is
$$ D(\bm{y},\bm{\mu})=\sum_{i=1}^m w_i d(y_i,\mu_i) $$
Where \(d(y_i,\mu_i)\) is the unit deviance of the
unifed distribution between the i-th entry of \(\bm{y}\) and
\(\bm{\mu}\). \(w_i\) is the i-th entry of the weight
vector. unifed.unit.deviance is used to get the value
of \(d\).
unifed.unit.deviance
unifed.unit.deviance uses the following expression
for the deviance of regular exponential dispersion families
$$ d(y,\mu)=2\left[y\{\dot{\kappa}^{-1}(y)-\dot{\kappa}^{-1}(\mu)\}-\kappa(\dot{\kappa}^{-1}(y))+\kappa(\dot{\kappa}^{-1}(\mu))\right]$$
\(\dot{\kappa}^{-1}\) is computed with the function
unifed.kappa.prime.inverse from this package.