families {aster}R Documentation

Families for Aster Models

Description

Families (response models) known to the package. In all functions families are specified by an integer index. families() returns names (as character strings) corresponding to valid index values. For each family three functions are defined: the cumulant function for the one-parameter exponential family, its first derivative (which maps canonical parameter to mean value parameter), and its second derivative (which maps canonical parameter to Fisher information).

Usage

families()
famfun(index, deriv, theta)

Arguments

index integer index of the family.
deriv derivative wanted: 0, 1, or 2.
theta value of the canonical parameter.

Details

Currently implemented families are

"bernoulli"
Bernoulli. The mean value parameter mu is the success probability. The canonical parameter is theta = log(mu) - log(1 - mu), also called logit of mu. The first derivative function has the value mu and the second derivative the value mu (1 - mu).
"poisson"
Poisson. The mean value parameter mu is the mean of the Poisson distribution. The canonical parameter is theta = log(mu). The first and second derivative functions both have the value mu.
"non.zero.poisson"
Poisson conditioned on being non-zero. Let mu be the mean of the unconditional Poisson distribution. The canonical parameter is theta = log(mu). The mean value parameter is

tau = mu / (1 - exp(- mu)

The first derivative function has the value tau and the second derivative function has the value tau [1 - tau * exp(- mu)].

Value

For families a vector of character strings, each a family name. For famfun a scalar double, the value.

Examples

families()
### mean of poisson with mean 0.2 conditioned on being nonzero
famfun(3, 1, log(0.2))
### variance of poisson with mean 0.2 conditioned on being nonzero
famfun(3, 2, log(0.2))

[Package aster version 0.4-1 Index]