I am new to the field, so forgive me for any silly questions. I am trying to assign probability distributions to my uncertain inputs, and the first probability distribution that comes to mind is the overused gaussian/normal distribution. Although, it has been suggested by multiple sources that Gaussian distributions should not be used for strictly positive random variables (RVs), I am still seeing a lot of peer-reviewed papers in the UQ-CFD field that are using gaussian distributions to such RVs. I would appreciate it if anybody can give some input on the matter.
Dear Elias
I would be cautious about using a Gaussian distribution simply because it is the default choice. If you do not have sufficient data or prior knowledge to justify a Gaussian model for your input, it is generally better to avoid it, especially when the variable is strictly positive.
In practical engineering, when data are limited, the choice of distribution is often guided by physical reasoning and engineering judgment. For variables related to capacity (e.g., material strength, resistance, dimensions), the lognormal distribution is commonly adopted because it is strictly positive and has been shown to fit many experimental datasets reasonably well. For variables related to loads or demands, extreme value distributions such as the Weibull, Gumbel, or Fréchet distributions are often more appropriate, depending on the nature of the loading.
There are two main reasons for these choices. First, they are supported by some experimental and field data and engineering literature. Second, and perhaps more importantly, they generally provide a more conservative representation of uncertainty and provide higher marginal safety.
So my suggestion is that don’t use a Gaussian distribution blindly. If your variable represents a strictly positive capacity parameter and you lack sufficient data, a lognormal distribution is usually a much better starting point.
If, for some reason, you still want to use a Gaussian distribution, consider using a truncated Gaussian distribution so that negative values cannot be generated.
Cheers