I am guessing that most component values follow a Gaussian (normal) distribution, but I wanted read this and make sure. Google proved not that helpful.

Also, what about capacitors, inductors, voltage sources, transistor parameters... is there any place to find the pdf (prime density function) of these distributions? Do they list it in the datasheets? Or is everything just assumed Gaussian?

 

I suspect you mean the probability density function, not prime density function.

It is convenient to assume things are normally distributed and often they are. However, the only way to know for sure is to measure. And even with measurements, that's no guarantee that the process producing the parts is in control and providing parts from the same distribution it did the week before.

You may find it nearly impossible to get manufacturers to disclose statistics characterizing their production processes' distributions. I'm out of touch with things today, but back in the 80's when I was doing lots of statistical type stuff (in conjunction with bringing up a thin film disk manufacturing facility), there were two main reasons: the manufacturers didn't know or they considered it proprietary. One of the reasons for considering it proprietary was because they were ashamed of their process capabilities. Another is that they don't want their competitors to know. It also can take a lot of work to do a proper characterization.

You also want to be careful assuming a normal (or any) distribution for products that are high tech and are accepted or rejected at a final inspection in manufacturing. If there's significant measurement error involved, you'll potentially be looking at both truncated distributions and significant type 1 and type 2 errors.

If you're a small customer, your chances of getting process information may be pretty small. You're a lot better off if you're doing $100k-$1M or more per month with that vendor.