Indeed, "estimations" might not be the best word as you're still, in some way, estimating with the Monte Carlo approach. I thought of this differentiation because I consider the MC approach to yield a forecast, while an "estimation" is the typical term used in agile settings for "guessing how long/much work it will take.". I'll think of ways of making this distinction clearer.
As for the misused mathematical terminology I guess you're referring to "confidence intervals"? If so, I understand it also has a clear definition within statistics, but I used it in the broader sense. I'd be grateful if you could point out which terms you'd recommend replacing and what you think I could replace it for.
> Indeed, "estimations" might not be the best word as you're still, in some way, estimating with the Monte Carlo approach.
Not in some way -- literally. The samples are averaged, and as the number of samples goes to infinity, the average converges to some true value. In the case of one of the histograms you plot, you are averaging an indicator function .
> I thought of this differentiation because I consider the MC approach to yield a forecast, while an "estimation" is the typical term used in agile settings for "guessing how long/much work it will take.". I'll think of ways of making this distinction clearer.
It seems to me the distinction you care for is to provide not a single value ("estimate"), but a distribution of values. That's not specific to Monte Carlo.
> As for the misused mathematical terminology I guess you're referring to "confidence intervals"
That's certainly one of them. I even misunderstood what you were doing and said you don't need confidence intervals, but in the way you're using them those again can be obtained by quadrature.
My main gripe remains the language, and the presentation of the method. You could most likely obtain your results by hand, i.e. with pen and paper, and you would still get a distribution at the end of the day. The advantage of running Monte Carlo is that it simplifies this process. You could illustrate this by getting the distribution of the sum of two independent uniform random variables in two different ways: by doing a convolution, and by MC. Wow, MC was so much easier, anyone can do it, and it can handle arbitrarily complicated distributions (in principle).
Indeed, "estimations" might not be the best word as you're still, in some way, estimating with the Monte Carlo approach. I thought of this differentiation because I consider the MC approach to yield a forecast, while an "estimation" is the typical term used in agile settings for "guessing how long/much work it will take.". I'll think of ways of making this distinction clearer.
As for the misused mathematical terminology I guess you're referring to "confidence intervals"? If so, I understand it also has a clear definition within statistics, but I used it in the broader sense. I'd be grateful if you could point out which terms you'd recommend replacing and what you think I could replace it for.
Thanks a lot.