(see vglmff-class).
The object is used by modelling functions
such as vglm,
and vgam.
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.
Author
T. W. Yee
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.
References
Vaughan, D. C. (2002).
The generalized secant hyperbolic
distribution and its properties.
Communications in Statistics---Theory
and Methods,
31(2): 219--238.