Partial density component (PDC) estimator
Description
The partial density component (PDC) estimator estimates the shape parameter of a Pareto distribution based on the relative excesses of observations above a certain threshold.
Usage
1 
Arguments
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. 
w 
an optional numeric vector giving sample weights. 
... 
additional arguments to be passed to

Details
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 PDC estimator minimizes the integrated squared error (ISE) criterion with
an incomplete density mixture model. The minimization is carried out using
nlm
. By default, the starting value is obtained with
the Hill estimator (see thetaHill
).
optimize
.
Value
The estimated shape parameter.
Note
The arguments x0
for the threshold (scale parameter) of the
Pareto distribution and w
for sample weights were introduced in
version 0.2.
Author(s)
Andreas Alfons and Josef Holzer
References
A. Alfons and M. Templ (2013) Estimation of Social Exclusion Indicators from Complex Surveys: The R Package laeken. Journal of Statistical Software, 54(15), 1–25. URL http://www.jstatsoft.org/v54/i15/
A. Alfons, M. Templ, P. Filzmoser (2013) Robust estimation of economic indicators from survey samples based on Pareto tail modeling. Journal of the Royal Statistical Society, Series C, 62(2), 271–286.
Vandewalle, B., Beirlant, J., Christmann, A., and Hubert, M. (2007) A robust estimator for the tail index of Paretotype distributions. Computational Statistics & Data Analysis, 51(12), 6252–6268.
See Also
paretoTail
, fitPareto
,
thetaISE
, thetaHill
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13  data(eusilc)
# equivalized disposable income is equal for each household
# member, therefore only one household member is taken
eusilc < eusilc[!duplicated(eusilc$db030),]
# estimate threshold
ts < paretoScale(eusilc$eqIncome, w = eusilc$db090)
# using number of observations in tail
thetaPDC(eusilc$eqIncome, k = ts$k, w = eusilc$db090)
# using threshold
thetaPDC(eusilc$eqIncome, x0 = ts$x0, w = eusilc$db090)
