How to average CDFs of one variable across years I have wealth-to-income data for 10 years. I computed the cdf of this variable in each year.
Now I'm trying to average the cdfs across years. In each each, the number of observations is different.
Does anyone know how to do it?
Thank you in advance.
Susan
Why don't you just take a weighted average?
Suppose you have ten years $t \in \{1,...,10\}$ and year $t$ has $N_t$ observations such that in total you have $\sum_t N_t=N$ observations. Let the year-$t$ CDF be $F_t$ with support $[\underline w_t,\overline w_t]$.
You can then define a weighted average CDF as
$$\overline F (w) = \sum_t \frac{N_t}{N} F_t(w).$$
This gives you a cdf, an increasing right-continuous function ranging over [0,1] with support $\cup_t [\underline w_t,\overline w_t]$. However, you have to pay attention to the individual supports, i.e., $F_t(w) =1 \forall w&gt;\overline w_t$ and $F_t(w) =0 \forall w&lt;\underline w_t$.