VGAM (version 1.1-9)

logF: Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

Description

Maximum likelihood estimation of the 2-parameter log F distribution.

Usage

logF(lshape1 = "loglink", lshape2 = "loglink",
      ishape1 = NULL, ishape2 = 1, imethod = 1)

Value

An object of class "vglmff" (see

vglmff-class). The object is used by modelling functions such as vglm and vgam.

Arguments

lshape1, lshape2

Parameter link functions for the shape parameters. Called \(\alpha\) and \(\beta\) respectively. See Links for more choices.

ishape1, ishape2

Optional initial values for the shape parameters. If given, it must be numeric and values are recycled to the appropriate length. The default is to choose the value internally. See CommonVGAMffArguments for more information.

imethod

Initialization method. Either the value 1, 2, or .... See CommonVGAMffArguments for more information.

Author

Thomas W. Yee

Details

The density for this distribution is $$f(y; \alpha, \beta) = \exp(\alpha y) / [B(\alpha,\beta) (1 + e^y)^{\alpha + \beta}] $$ where \(y\) is real, \(\alpha > 0\), \(\beta > 0\), \(B(., .)\) is the beta function beta.

References

Jones, M. C. (2008). On a class of distributions with simple exponential tails. Statistica Sinica, 18(3), 1101--1110.

See Also

dlogF, extlogF1, logff.

Examples

nn <- 1000
ldata <- data.frame(y1 = rnorm(nn, +1, sd = exp(2)),  # Not proper data
                    x2 = rnorm(nn, -1, sd = exp(2)),
                    y2 = rnorm(nn, -1, sd = exp(2)))  # Not proper data
fit1 <- vglm(y1 ~ 1 , logF, ldata, trace = TRUE)
fit2 <- vglm(y2 ~ x2, logF, ldata, trace = TRUE)
coef(fit2, matrix = TRUE)
summary(fit2)
vcov(fit2)

head(fitted(fit1))
with(ldata, mean(y1))
max(abs(head(fitted(fit1)) - with(ldata, mean(y1))))