I have a empirical cumulative probability distribution function for a random variable. The random variable is "time to failure" and I have the full curve i.e till the probability reaches $1$. I want to know Mean Time To Failure i.e expectation of that random variable. Is there any standard method to find mean from an empirical distribution.
I am getting the empirical CDF (as discrete values) as output from a "model checking tool" which uses iterative numerical computation techniques to get those probabilities. For example, let $F(t)=P(X \leq t)$ is the CDF of the random variable $X$ where $X$ stands for time between failure. To plot the curve of "$F(t)$ vs $t$" I am varying t with some step size, calculating $F(t)$ for that t using the "model checking tool" and adding the points to get the curve. I can use small step size to get the more accurate curve. So, I have access to only this CDF values at different$ t$. From this values I want to do a good estimate of mean value of $X$.
Now the parameters will be:
1) $T$, the maximum value of t. We need to find this with some precision i.e if $F(T_1)-F(T_2)$ is less than some epsilon we set $T=T_1$.
2) Once we have found T we need to find suitable step size $h$ at which we will be calculating the CDF values.
How should I choose those parametrs?