fitPareto: Fit income distribution models with the Pareto distribution

In aalfons/laeken: Estimation of Indicators on Social Exclusion and Poverty

Fit income distribution models with the Pareto distribution

Description

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.

Usage

fitPareto(
  x,
  k = NULL,
  x0 = NULL,
  method = "thetaPDC",
  groups = NULL,
  w = NULL,
  ...
)

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.
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 thetaPDC (the default). See “Details” for requirements for such a function and “See also” for available functions.
groups	an optional vector or factor specifying groups of elements of x (e.g., households). If supplied, each group of observations is expected to have the same value in x (e.g., household income). Only the values of every first group member to appear are used for fitting the Pareto distribution. For each group above the threshold, every group member is assigned the same value.
w	an optional numeric vector giving sample weights.
...	addtional arguments to be passed to the specified method.

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 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.

Value

A numeric vector with a Pareto distribution fit to the upper tail.

Note

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.

Author(s)

Andreas Alfons and Josef Holzer

See Also

paretoTail, replaceTail

thetaPDC, thetaWML, thetaHill, thetaISE, thetaLS, thetaMoment, thetaQQ, thetaTM

Examples

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)

aalfons/laeken documentation built on Feb. 9, 2024, 7:16 p.m.