# logF: Natural Exponential Family Generalized Hyperbolic Secant... In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2``` ``` logF(lshape1 = "loglink", lshape2 = "loglink", ishape1 = NULL, ishape2 = 1, imethod = 1) ```

## 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.

## Details

The density for this distribution is

f(y; alpha, beta) = exp(α y) / [B(α,β) * (1 + exp(y))^(α + β)]

where y is real, α > 0, β > 0, B(., .) is the beta function `beta`.

## Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm` and `vgam`.

Thomas W. Yee

## References

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

`dlogF`, `extlogF1`, `logff`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```nn <- 1000 ldata <- data.frame(y1 = rnorm(nn, m = +1, sd = exp(2)), # Not proper data x2 = rnorm(nn, m = -1, sd = exp(2)), y2 = rnorm(nn, m = -1, sd = exp(2))) # Not proper data fit1 <- vglm(y1 ~ 1 , logF, data = ldata, trace = TRUE) fit2 <- vglm(y2 ~ x2, logF, data = 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)))) ```