| unifed.deviance {unifed} | R Documentation |
Deviance of the unifed distribution
Description
Deviance of the unifed distribution
Usage
unifed.deviance(y.v, mu.v, wt = 1, ...)
unifed.unit.deviance(y, mu, tol = 1e-07, maxit = 50)
Arguments
y.v |
A numeric vector with values between 0 and 1 |
mu.v |
A numeric vector with values between 0 and 1 |
wt |
(default value: 1) The weight vector. It contains the weight of each observation. It must contain positive integers only. |
... |
Additional parameters of |
y |
A vector with values between 0 and 1. |
mu |
A vector with values between 0 and 1. |
tol |
Tolerance level for the Newton-Raphson algorithm for computing the inverse of the derivative of the cumulant generator of the family. |
maxit |
Maximum number of iterations for the Newton-Raphson algorithm for computing the inverse of the derivative of the cumulant generator of the family. |
Details
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.
Value
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