First off, it’s not a homework question; I’m trying to develop some software and have run up against the limits of my already limited stats knowhow.
I’m trying to generate a sequence of random numbers whose PDF is normal with some arbitrary mean and variation. I can get this far. However, I’d also like for each number to bear some relation to the one before, such that if one number is significantly above the mean, the next number is more likely to be so as well. I seem to have trouble describing this so have drawn an outstandingly amateurish picture to try and illustrate what I mean:
Does this make any sense at all? The vertical red line is the last number I generated, and the red distribution is what I’d like to use to generate the next number; I just have no idea what the maths behind it might be. As an example, if the previous number were exactly the mean of the overall distribution, the next number would be unaffected. I just want a slower return to the mean value after outliers, without affecting the overall distribution after many numbers have been generated. So the question really is; what on earth function did I just draw? Does it exist outside my brain?
Any help would be greatly appreciated…