I am calculating emissions considering the uncertainty of the data to do Monte Carlo simulation. Some variables such as yields have normal, lognormal or even uniform distributions. These must be multiplied by emission factors of which I only know their minimum, maximum and most probable value, so I assume that their distribution is triangular. How can I do this operation?
This might help:
https://www.mathworks.com/help/stats/generate-random-numbers-using-a-triangular-probability-distribution-object.html
If you asking how to generate random numbers with a triangular distribution between a & b, and with the peak of the triangle at (a+b)/2:
An easy trick is to generate two uniform random numbers, each one ranging from a/2 to b/2. Then add those two uniforms, and their sum will have the desired triangular distribution from a to b.
You need minimum, maximum and peak values to know if the emission distributions are triangular. The minimum value must be less than or equal to the peak value, which in turn must be equal to or less than the maximum value. Your most probable value is your peak value. The mean value is the sum of the three parameters divided by 3 and standard deviation is 0.41 x the minimum value
https://www.statisticshowto.com/triangular-distribution/
Sounds like you need the formula for a Product Distribution: https://en.wikipedia.org/wiki/Product_distribution https://en.wikipedia.org/wiki/Algebra_of_random_variables
Here is a not-very-good video I made on the Ratio Distribution a while back, you can take the R code seen on the screen and just tweak the formula for a ratio distribution.
https://www.youtube.com/watch?v=UtEY9cQhe7U
Dear Dr , you may find some answers here
https://math.stackexchange.com/questions/72964/combining-two-triangular-distributions-to-yield-one-distribution
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