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mathdude2018
Topic Author
Posts: 14
Joined: January 10th, 2018, 4:35 pm

### Scaling/Shifting an empirical distribution

I am generating 500 points in Monte Carlo distribution based on some empirical/historical behavior. However, the mean is different from what we see in the forward market. We need to readjust the mean of this distribution to that displayed by forward market.

This is a non parametric distribution i.e. just a bunch of data points. How do I adjust the distribution so that new distribution has the desired mean from forward market.

Does it need some kind of entropy minimization approach?

Alan
Posts: 10714
Joined: December 19th, 2001, 4:01 am
Location: California
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### Re: Scaling/Shifting an empirical distribution

$x'_i = x_i - \mu + \mu'$

bearish
Posts: 6638
Joined: February 3rd, 2011, 2:19 pm

### Re: Scaling/Shifting an empirical distribution

Aside from the low sample size, there is also an intended change of measure taking place here. It is possible that if we knew a bit more about the nature of your problem we could be more helpful. Like, maybe a multiplicative adjustment could be more appropriate than Alan’s additive one. Or, I guess, you could just take logs as needed.