unifed.deviance: Deviance of the unifed distribution

In unifed: 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 unifed.kappa.prime.inverse.one
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

- 1 - 1 - 1 - 1 d(y,mu) = 2[y( (k') (y) - (k') (mu) ) - k((k') (y)) + k((k') (mu))].

(k')^(-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

__ m D(y,mu) = \ w_i d(y_i ,mu_i ) /__ i = 1

Where d(y_i,mu_i) is the unit deviance of the unifed distribution between the i-th entry of y and 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 documentation built on Jan. 31, 2022, 1:07 a.m.