# Is there a term to refer to a weighted mean that's weighted by a function of percentile (using a kernel)?

I came-up with a type of central tendency which is a weighted mean. The weighting is based on percentile, with values closer to the median having a higher weight. It's similar to the idea of a truncated mean, but it's a soft approach to dealing with outliers. For example, if x is the percentile of each value in the set, the weights can be determined with these 3 functions

x(x-1)
(x(x-1))²
(x(x-1))³


I'm sure I'm not the first to come-up with this. Is there an existing term for this kind of central tendency?

• Presumably you are using $x(1-x)$ or its powers – Henry Feb 13 '19 at 20:02
• A normalized form for those weights is $x^n(1-x)^n(2n+1)!/(n!)^2$ – Matt F. Oct 6 '19 at 0:08

## 1 Answer

Weightings based on percentiles also occur in rank-dependent expected utility (RDEU), so you could call these rank-dependent weightings or rank-dependent expectations.