I came across this function in a paper (used to compute the distribution of some real-valued random variable $\lambda_{c}$):
$$\large f({\lambda})=\sum\limits_{c \in C_{S}} \frac{\chi_{\{\lambda\}}(\lambda_{c})}{\#(C_{S})}$$
$\lambda$ is a logit value calculated from two probability values (i.e., $\lambda=ln\frac{p}{1-p}$, where p is some probability value); for each $c$, there's one and only one logit value. The distribution of $\lambda$ is unknown and not assumed before hand; it may vary depending on the configuration of original model.
$\chi$ is the characteristic function (quote the paper, it was actually characterization function) for $\lambda$;
$C_{S}$ represents all the possible combinations if we choose $k=S/2$ items from $S$ items;
$c$ accordingly refers to a single combination in $C_{S}$, where $c \in C_{S}$;
$\#(C_{S})$ effectively denotes the total number of combinations.
I don't understand the use of characteristic function here. Given the distribution of $\lambda$ is unknown before hand (and can be estimated from observations), to capture the $pdf$ of some $r.v.$ like $\lambda$, do mathematicians use characteristic function for contingency? Or is there a particular reason for the use of characteristic function in this case?
here's a link to the paper and the formulae is towards the end of page 12. The contextual information was on page 10-11.
If there's more information needed please let me know.