R: Fit income distribution models with the Pareto distribution

fitPareto {laeken} | R Documentation

## 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)

[Package laeken version 0.4.6 Index]