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<=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(T1)-F(T2) is less than some epsilon we set T=T1.
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?