I'd like to add something which the other answers haven't mentioned yet.
It is true that a gaussian distribution is not the same thing as a uniform white-noise distribution. They can be related however. True white noise occurs in a resistor as a result of the brownian motion.
It kind of implies that the imaginary part of a complex resistance is zero: in
a + ib,
b has to equal 0.
Non-zero imaginary are caused by capacitance / inductivities, and will cause low-pass or high-pass behaviour, and thus, the spectral distribution is no longer uniform, but still "linear"
However, non-linear components, such as diodes, can shape a uniform distribution in a way that it becomes a gaussian distributed random value. Or any other distribution, depending on what non-linearity is at play.
Because from an engineering perspective, it sometimes is not very important how the spectral composition looks like, we may want to calculate one number to express a noise level instead. This can done by integrating over the whole (or parts of the) spectrum.
Afterwards, it is impossible to tell wheter the integrated value came from what was originally gaussian, or uniform, or anything else.
Assuming we integrated over a a gaussian distribution, we can always find an uniform distribution that is scaled so that its integral matches the integral of our gaussian distribution.
This has immediate merit for our calculations: We can then assume a complex non-linear component is just a resistance after all, which may simplify calculations. I recall that sometimes this is done by the manufacturer already and being given in the datasheet.