unifed {unifed}

Family object for the unifed distribution

Description

Family object for the unifed distribution

Usage

unifed(link = "logit", ...)

quasiunifed(link = "logit", ...)

unifed.canonical.link()

Arguments

link

a specification for the model link function. This can be a name/expression, a literal character string, a length-one character vector or an object of class ‘"link-glm"’ (such as generated by ‘make.link’) provided it is not specified via one of the accepted names. The unifed family accepts the links (as names) 'canonical', 'logit', 'probit', 'cloglog' and 'cauchit'.

...

Optional tol and maxit arguments for unifed.unit.deviance.

Details

The link 'canonical' is not part of the standard names accepted by make.link() from the stats package. It corresponds to the canonical link function for the unifed distribution, which is the inverse of the derivative of its cumulant generator. There is no explicit formula for it. The function unifed.kappa.prime.inverse() implements it using the Newthon-Raphson method.

This function is used inside of unifed() when the link parameter is set to "canonical". It returns the link function, inverse link function, the derivative dmu/deta and a function for domain checking for the unifed distribution canonical link.

Value

unifed returns a family object for using the unifed distribution with the glm function.

The quasiunifed family differs from the unifed only in that the dispersion parameter is not fixed to one.

An object of class "link-glm".

References

Jørgensen, Bent (1992). The Theory of Exponential Dispersion Models and Analysis of Deviance. Instituto de Matemática Pura e Aplicada, (IMPA), Brazil.

Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss—Newton method. Biometrika. 61 (3): 439–447.

McCullagh, Peter; Nelder, John (1989). Generalized Linear Models (second ed.). London: Chapman and Hall.

See Also

Gamma unifed.kappa.prime.inverse

make.link