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cauchy(llocation="identity", lscale="loge", elocation=list(),
escale=list(), ilocation=NULL, iscale=NULL,
iprobs = seq(0.2, 0.8, by=0.2),
method.init=1, nsimEIM=NULL, zero=2)
cauchy1(scale.arg=1, llocation="identity",
elocation=list(), ilocation=NULL, method.init=1)
Links
for more choices.earg
in Links
for general information.ilocation
iscale
.CommonVGAMffArguments
for more information."vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.method.init
, ilocation
, iscale
etc.nsimEIM
is specified then
Fisher scoring with simulation is used. If the scale parameter is known (cauchy1
) then there
may be multiple local maximum likelihood solutions for the location
parameter. However, if both location and scale parameters are to
be estimated (cauchy
) then there is a unique maximum
likelihood solution provided $n > 2$ and less than half the data
are located at any one point.
Barnett, V. D. (1966) Evaluation of the maximum-likehood estimator where the likelihood equation has multiple roots. Biometrika, 53, 151--165.
Copas, J. B. (1975) On the unimodality of the likelihood for the Cauchy distribution. Biometrika, 62, 701--704.
Efron, B. and Hinkley, D. V. (1978) Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information. Biometrika, 65, 457--481.
Cauchy
,
cauchit
.# Both location and scale parameters unknown
nn <- 1000
cdata1 = data.frame(x = runif(nn))
cdata1 = transform(cdata1, loc=exp(1+0.5*x), scale=exp(1))
cdata1 = transform(cdata1, y = rcauchy(nn, loc, scale))
fit = vglm(y ~ x, cauchy(lloc="loge"), cdata1, trace=TRUE)
coef(fit, matrix=TRUE)
head(fitted(fit)) # Location estimates
summary(fit)
# Location parameter unknown
set.seed(123)
cdata2 = data.frame(x = runif(nn <- 500))
cdata2 = transform(cdata2, loc=1+0.5*x, scale=0.4)
cdata2 = transform(cdata2, y = rcauchy(nn, loc, scale))
fit = vglm(y ~ x, cauchy1(scale=0.4), cdata2, trace=TRUE, crit="c")
coef(fit, matrix=TRUE)
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