thetaMoment: Moment estimator
In laeken: Estimation of Indicators on Social Exclusion and Poverty

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Estimate the shape parameter of a Pareto distribution based on moments.

1	thetaMoment(x, k = NULL, x0 = 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.

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 estimated shape parameter.

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

Andreas Alfons and Josef Holzer

Dekkers, A.L.M., Einmahl, J.H.J. and de Haan, L. (1989) A moment estimator for the index of an extreme-value distribution. The Annals of Statistics, 17(4), 1833–1855.

paretoTail, fitPareto

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

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