lgammaff {VGAM} | R Documentation |
Estimation of the parameter of the standard and nonstandard log-gamma distribution.
lgammaff(link = "loge", earg=list(), init.k = NULL) lgamma3ff(llocation="identity", lscale="loge", lshape="loge", elocation=list(), escale=list(), eshape=list(), ilocation=NULL, iscale=NULL, ishape=1, zero=NULL)
llocation |
Parameter link function applied to the
location parameter a.
See Links for more choices.
|
lscale |
Parameter link function applied to the
positive scale parameter b.
See Links for more choices.
|
link, lshape |
Parameter link function applied to
the positive shape parameter k.
See Links for more choices.
|
earg, elocation, escale, eshape |
List. Extra argument for each of the links.
See earg in Links for general information.
|
init.k, 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.
|
The probability density function of the standard log-gamma distribution is given by
f(y) = 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.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
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 lgammaff
and the non-standard (3-parameter) log-gamma distribution is fitted
with lgamma3ff
.
T. W. Yee
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.
rlgamma
,
ggamma
,
prentice74
,
gamma1
,
lgamma
.
ldat = data.frame(y = rlgamma(nn <- 100, k=exp(1))) fit = vglm(y ~ 1, lgammaff, ldat, trace=TRUE, crit="c") summary(fit) coef(fit, matrix=TRUE) Coef(fit) ldat = data.frame(x = runif(nn <- 5000)) # Another example ldat = transform(ldat, loc = -1 + 2*x, Scale = exp(1+x)) ldat = transform(ldat, y = rlgamma(nn, loc=loc, scale=Scale, k=exp(0))) fit = vglm(y ~ x, lgamma3ff(zero=3), ldat, trace=TRUE, crit="c") coef(fit, matrix=TRUE)