fitPareto  R Documentation 
Fit a Pareto distribution to the upper tail of income data. Since a theoretical distribution is used for the upper tail, this is a semiparametric approach.
fitPareto(
x,
k = NULL,
x0 = NULL,
method = "thetaPDC",
groups = NULL,
w = NULL,
...
)
x 
a numeric vector. 
k 
the number of observations in the upper tail to which the Pareto distribution is fitted. 
x0 
the threshold (scale parameter) above which the Pareto distribution is fitted. 
method 
either a function or a character string specifying the function
to be used to estimate the shape parameter of the Pareto distibution, such as

groups 
an optional vector or factor specifying groups of elements of

w 
an optional numeric vector giving sample weights. 
... 
addtional arguments to be passed to the specified method. 
The arguments k
and x0
of course correspond with each other.
If k
is supplied, the threshold x0
is estimated with the n
 k
largest value in x
, where n
is the number of observations.
On the other hand, if the threshold x0
is supplied, k
is given
by the number of observations in x
larger than x0
. Therefore,
either k
or x0
needs to be supplied. If both are supplied,
only k
is used (mainly for back compatibility).
The function supplied to method
should take a numeric vector (the
observations) as its first argument. If k
is supplied, it will be
passed on (in this case, the function is required to have an argument called
k
). Similarly, if the threshold x0
is supplied, it will be
passed on (in this case, the function is required to have an argument called
x0
). As above, only k
is passed on if both are supplied. If
the function specified by method
can handle sample weights, the
corresponding argument should be called w
. Additional arguments are
passed via the ... argument.
A numeric vector with a Pareto distribution fit to the upper tail.
The arguments x0
for the threshold (scale parameter) of the
Pareto distribution and w
for sample weights were introduced in
version 0.2. This results in slightly different behavior regarding the
function calls to method
compared to prior versions.
Andreas Alfons and Josef Holzer
paretoTail
, replaceTail
thetaPDC
, thetaWML
, thetaHill
,
thetaISE
, thetaLS
, thetaMoment
,
thetaQQ
, thetaTM
data(eusilc)
## gini coefficient without Pareto tail modeling
gini("eqIncome", weights = "rb050", data = eusilc)
## gini coefficient with Pareto tail modeling
# using number of observations in tail
eqIncome < fitPareto(eusilc$eqIncome, k = 175,
w = eusilc$db090, groups = eusilc$db030)
gini(eqIncome, weights = eusilc$rb050)
# using threshold
eqIncome < fitPareto(eusilc$eqIncome, x0 = 44150,
w = eusilc$db090, groups = eusilc$db030)
gini(eqIncome, weights = eusilc$rb050)
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