This may sound like a noob question but I'm unable to find any 'good' resources/examples on the same. The basic question is this: Most variables, depending on the problem will follow certain types of distributions. Normal/Gaussian may not be the most appropriate one for capturing certain types of phenomena.
Although I'm quite familiar with various distributions from a mathematical viewpoint I'm unable to understand some of them conceptually e.g.: Uniform distribution is when the occurrence of that event is equally likely over time, Normal when the occurrence 'tends' to be centered around the mean more often (like number of defects in samples or heights of citizens in a country etc.,) Similarly for triangular – I understand these easy ones so to speak.
What type of distributions have you commonly encountered when using monte-carlo simulations? Examples would be helpful along with the rationale for choosing that distribution. Basically looking for a reference/pointer that would help me lay it out as a list for reference and understanding. I'd prefer a non-mathematical explanation since it'll be used for discussing with non-mathematical stakeholders to whom the monte-carlo simulations would be shown
- <"Distribution name"> : <"Most appropriate use">
I've heard of the power law but don't really know/understand what it is and how it could be used.
Best Answer
The books "Continuous univariate distributions" Vol 1 + Vol 2 by Johnson, Kotz and Balakrishnan (and there is a multivariate book too, I believe) are classical references, rich on the mathematical properties as well as giving examples of the usages of the different distributions they treat.
If you want details on a specific class of distributions, Wikipedia is always a good place to start, see
http://en.wikipedia.org/wiki/Power_law
The requested list is probably not easy to compile - the "most appropriate use" may be highly dependent upon context, but again the Wikipedia list of distributions
http://en.wikipedia.org/wiki/List_of_probability_distributions
could be a place to start to find distributions appropriate for your project.