Calculation of a Huber-type correction factor by which the vector of weights is multiplied.
robwts(x, w=rep(1,length(x)), c=0.01, alpha=0.001)numeric; vector of data values.
numeric; vector of weights. Must have the same length as x. By default w is a vector of 1.
numeric; a constant which can take different values, e.g. 0.01,0.02. By default \(c=0.1\).
numeric; a probability in the interval \((0,1)\). By default \(alpha=0.001\).
robwts returns a list of two elements: the vector of correction factors by which the weights are multiplied and the vector of corrected (robustified) weights.
If \(x\) denotes the observed value and \(x_{\alpha}\) the \(\alpha\)-th qiantile of the Fisk distribution, then we define our scale as: $$d = \displaystyle \frac{x_{1-\alpha}}{b} - \frac{x_{\alpha}}{b}$$. Next, the correction factor is calculated as follows: $$corr = \max\left\{c, \min\left(1,\displaystyle \frac{d}{|b/x-1|},\frac{d}{|x/b-1|}\right)\right\}$$
Graf, M., Nedyalkova, D., Muennich, R., Seger, J. and Zins, S. (2011) AMELI Deliverable 2.1: Parametric Estimation of Income Distributions and Indicators of Poverty and Social Exclusion. Technical report, AMELI-Project.