Parameter link function applied to the
location parameter a
and the positive scale parameter b.
See Links for more choices.
lshape
Parameter link function applied to
the positive shape parameter k.
See Links for more choices.
ishape
Initial value for k.
If given, it must be positive.
If failure to converge occurs, try some other value.
The default means an initial value is determined internally.
ilocation, iscale
Initial value for a and b.
The defaults mean an initial value is determined internally for each.
zero
An integer-valued vector specifying which
linear/additive predictors are modelled as intercepts only.
The values must be from the set {1,2,3}.
The default value means none are modelled as intercept-only terms.
See CommonVGAMffArguments for more information.
Details
The probability density function of the standard log-gamma distribution
is given by
f(y;k) = exp[ky - exp(y)]/gamma(k),
for parameter k>0 and all real y.
The mean of Y is digamma(k) (returned as
the fitted values) and its variance is trigamma(k).
For the non-standard log-gamma distribution, one replaces y
by (y-a)/b, where a is the location parameter
and b is the positive scale parameter.
Then the density function is
f(y) = exp[k(y-a)/b - exp((y-a)/b)]/(b*gamma(k)).
The mean and variance of Y are a + b*digamma(k) (returned as
the fitted values) and b^2 * trigamma(k), respectively.
Value
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Note
The standard log-gamma distribution can be viewed as a
generalization of the standard type 1 extreme value density:
when k = 1 the distribution of -Y is the standard
type 1 extreme value distribution.
The standard log-gamma distribution is fitted with lgamma1
and the non-standard (3-parameter) log-gamma distribution is fitted
with lgamma3.
Author(s)
T. W. Yee
References
Kotz, S. and Nadarajah, S. (2000)
Extreme Value Distributions: Theory and Applications,
pages 48–49,
London: Imperial College Press.
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1995)
Continuous Univariate Distributions,
2nd edition, Volume 2, p.89,
New York: Wiley.