# How to characterize the randomness of an event using it's PSD?

I have the power spectral density function of a stochastic phenomenon.

1. how can I generate a signal (time series) representing the randomness of this event over time?
2. How can I draw the probability distribution and commutative distribution functions from the given PSD in order to take N samples using the basic monte Carlo method?

The answer of (2) can be used to model the uncertainty of an event to use in Stochastic programming. We should get N samples, with an equal probability of 1/N.

The answer to (1) can be used to evaluate the given results of the stochastic programming by out-of-sample analysis.

Since I am not so familiar with Signal Processing notations, it would better to have the answer in form of an algorithm or Matlab/Python code, if possible.

• Is the "stochastic phenomenon / event" something like a pulse? In other words, is it something that happens at random intervals or is it a continuous stochastic signal? – A_A Sep 14 '20 at 9:21
• I want to model the uncertainty of wind speed variations for 1 hour. So, I think (but not sure) it's a continuous stochastic signal. @A_A – SAH Sep 14 '20 at 9:29
• 1) You can try the answer given here for the same problem: researchgate.net/post/… 2) Once you have the time-series, you can estimate its PDF (Matlab has functions to do so). You can then even use this PDF to generate new time sequences by transforming a uniform random sequence. You should find user codes in mathworks as well. en.wikipedia.org/wiki/… – danipascual Sep 14 '20 at 14:00