What is a characterisation function I am reading a paper: "Probability of Backtest Overfitting", and page 13 defines the relative frequency:

$$f(\lambda) = \sum_{c \in C_S} \frac{\chi_{\{\lambda\}} \left( \lambda_c\right)}{|\{C_S\}|}$$

the authors say that $\mathcal{X}$ is the characterization function. I would like to know what exactly that is since I have never come across that term before.

EDIT: I emailed the author of the paper, and according to him, $f(\lambda)$ is simply a PDF.
@i-squared-keep-it-real, 

hello, I saw your edit but the fact $f(\lambda)$ is PDF still does not give a clue about what the $\chi$ is? 

Should we solve the $\chi$ given the constraint $\int f(\lambda)d\lambda=1$ assuming $\chi$  is some type of function or should we fit something like Gaussian distribution to the frequency distribution ? 

I mean without the $\chi$ how can I compute the $f(\lambda)$ to access to the POB?

Looking forward to an update!!

Thanks a lot!!

Sorry that I cannot comment...
@i-squared-keep-it-real, 

hello, I saw your edit but the fact $f(\lambda)$ is PDF still does not give a clue about what the $\chi$ is? 

Should we solve the $\chi$ given the constraint $\int f(\lambda)d\lambda=1$ assuming $\chi$  is some type of function or should we fit something like Gaussian distribution to the frequency distribution ? 

I mean without the $\chi$ how can I compute the $f(\lambda)$ to access to the POB?

Looking forward to an update!!

Thanks a lot!!

Sorry that I cannot comment...