R: QQ-estimator

thetaQQ {laeken} | R Documentation

## QQ-estimator

### Description

Estimate the shape parameter of a Pareto distribution using a quantile-quantile approach.

### Usage

    thetaQQ(x, k = NULL, x0 = 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.

### 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).

### Value

The estimated shape parameter.

### Note

The argument `x0` for the threshold (scale parameter) of the Pareto distribution was introduced in version 0.2.

### Author(s)

Andreas Alfons and Josef Holzer

### References

Kratz, M.F. and Resnick, S.I. (1996) The QQ-estimator and heavy tails. Stochastic Models, 12(4), 699–724.

### See Also

`paretoTail`, `fitPareto`

### Examples

    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
    thetaQQ(eusilc$eqIncome, k = ts$k)

    # using threshold
    thetaQQ(eusilc$eqIncome, x0 = ts$x0)

[Package laeken version 0.4.6 Index]