gensh: Generalized Secant Hyperbolic Regression Family Function

In VGAM: Vector Generalized Linear and Additive Models

Generalized Secant Hyperbolic Regression Family Function

Description

Estimation of the parameters of the generalized secant hyperbolic distribution.

Usage

gensh(shape, llocation = "identitylink",
      lscale = "loglink", zero = "scale",
      ilocation = NULL, iscale = NULL, imethod = 1,
      glocation.mux = exp((-4:4)/2),
      gscale.mux = exp((-4:4)/2),
      probs.y = 0.3, tol0 = 1e-4)

Arguments

shape	Numeric of length 1. Shape parameter, called t in Vaughan (2002). Valid values are -\pi/2 < t.
llocation, lscale	Parameter link functions applied to the two parameters. See Links for more choices. See CommonVGAMffArguments for more information.
zero, imethod	See CommonVGAMffArguments for information.
ilocation, iscale	See CommonVGAMffArguments for information.
glocation.mux, gscale.mux	See CommonVGAMffArguments for information.
probs.y, tol0	See CommonVGAMffArguments for information.

Details

The probability density function of the hyperbolic secant distribution is given by

f(y; a, b, s) = [(c_1 / b) \; \exp(c_2 z)] / [ \exp(2 c_2 z) + 2 C_3 \exp(c_2 z) + 1]

for shape parameter -\pi < s and all real y. The scalars c_1, c_2, C_3 are functions of s. The mean of Y is the location parameter a (returned as the fitted values). All moments of the distribution are finite.

Further details about the parameterization can be found in Vaughan (2002). Fisher scoring is implemented and it has a diagonal EIM. More details are at Gensh.

Value

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

Author(s)

T. W. Yee

References

Vaughan, D. C. (2002). The generalized secant hyperbolic distribution and its properties. Communications in Statistics—Theory and Methods, 31(2): 219–238.

See Also

hypersecant, logistic.

Examples

sh <- -pi / 2; loc <- 2
hdata <- data.frame(x2 = rnorm(nn <- 200))
hdata <- transform(hdata, y = rgensh(nn, sh, loc))
fit <- vglm(y ~ x2, gensh(sh), hdata, trace = TRUE)
coef(fit, matrix = TRUE)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.