  The continuous time random walk model plays an important role in modeling of
so called anomalous diffusion behaviour. One of the specific property of such
model are constant time periods visible in trajectory. In the continuous time
random walk approach they are realizations of the sequence called waiting
times. The main attention of the paper is paid on the analysis of waiting times
distribution. We introduce here novel methods of estimation and statistical
investigation of such distribution. The methods are based on the modified
cumulative distribution function. In this paper we consider three special cases
of waiting time distributions, namely $\alpha$-stable, tempered stable and
gamma. However the proposed methodology can be applied to broad set of
distributions - in general it may serve as a method of fitting any distribution
function if the observations are rounded. The new statistical techniques we
apply to the simulated data as well as to the real data describing $CO_2$
concentration in indoor air.
