How to weight samples in a "skewed" way?!

[hellohere]

Say I have a sample of 100 people, and have their annual income in last 20 years. 

It is OK to calculate the average annual income.

NOW I like to calculate the "skewed" average income by year.  1) to skew to the high-income side 2) to skew to the low-income side. 

How to put "meaningful" weights on samples?  "meaningful" just need a) skew to the desired side  and b) sum to 100%.

[ballardw]

What rules do you have for "skewwing" the weights? As in how much?

Lots of ways to do this, many may not make sense.

Example dummy code:

Proc sort data=have;
   by income;
run;

data reweight;
   set have nobs=sampsize;
   weight = _n_ / sampsize;
run;

Will assign a smaller weight to the smaller incomes and the largest will have a weight of 1.

Then use Proc Means/Summary or just about any analysis procedure that supports uses of weight variables.

So do you have any rule(s) about how much you want to skew these values?

[hellohere]

This makes sense.

In term of how much, that is up to play to find the opt.

Better off without sorting/indexing/averaging.

In that case, how to do if the values can be negative or positive, say a normal t-distribution randoms, the average is non-zero and unknow. 

Need skew to left(low-end), without sorting/indexing, how to put weight(just on the value itself) ?!

[ballardw]

Not seeing much in the way of any rules to use. How much to skew>

Which values have to be negative or positive? The input or the output?

Some information you may want peruse:

https://support.sas.com/resources/papers/proceedings16/7660-2016.pdf

https://blogs.sas.com/content/iml/2022/09/21/noncentral-t.html

https://communities.sas.com/t5/SAS-IML-Software-and-Matrix/Skew-Normal-Distributions/td-p/145628

BTW setting restriction of not sorting or averaging data is may quite well be impractical to impossible depending on a specific task.