Simulating distributions I am working on a Capacity Planning assignment and I have read some books. This is specifically about distributions. I use R.

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*What is the recommended approach to identify what my data distribution is ? Are there statistical methods to identify it ?

I have this diagram.



*What are simulations approaches available using R ? Here I want to generate data for a certain distribution like exponential. Is r-java the right approach if I want to integrate it with Java ?


*Is there a way to predict what distribution the effect( CPU usage etc. ) will have when I pipe data for a particular distribution ? What are the different effects of sending certain distributions of data ?
Please consider these as beginner's questions. Are there books or material that deal with these types of simulations ?
Notes
THe diagram is from the end of the paper http://people.stern.nyu.edu/adamodar/pdfiles/papers/probabilistic.pdf.
Goodness of fit techniques I have come across
Assessment of goodness-of-fit

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*Chi-squared

*Kolmogorov-Smirnov,

*Anderson-Darling statistics density, cdf, P-P and Q-Q plots

I am not sure what the interpretation or next steps should be if I find that my distribution is normal or exponential etc. What does it allow me to do? Prediction? Hope this question is clear.
Exponential delays will induce queue fluctuatuions as per my Capacity Planning book by Neil Gunther. So I know that one point.
 A: I will answer your point about simulations with R because this is the only one I am familiar with. R has a lot of builtin distributions which you can simulate. The logics of naming is that to simulate a distribution called dis the name will be rdis.
Below are the ones I use most often
# Some continuous distributions.
?rnorm
?runif
?rgamma
?rlnorm
?rweibull
?rexp
?rt
# Some discrete distributions.
?rpoiss
?rbinom
?rnbinom
?rgeom
?rhyper

You can find some complements in Fitting distributions with R.
Addition: thanks to @jthetzel for providing a link with a comprehensive list of distributions and the packages they belong to.
But wait, there's more: OK, following @whuber's comment I'll try to address the other points. Regarding point 1, I never go by a goodness-of-fit approach. Instead I always think about the origin of the signal, like what causes the phenomenon, is there some natural symmetries in what produces it etc. You need several book's chapters to cover it so I'll just give two examples.


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*If the data are counts and there is no upper limit, I try a Poisson. Poisson variables can be interpreted as the counts of successive independent during a time window, which is a very general framework. I fit the distribution and see (often visually) whether the variance is well described. Quite often, the variance of the sample is much higher, in which case I use a Negative Binomial. Negative Binomial can be interpreted as a mix of Poisson with different variables, which is even more general, so this usually fits very well to the sample.

*If I think that the data is symmetric around the mean, i.e. that deviations are equally likely to be positive or negative, I try to fit a Gaussian. I then check (again visually) whether there is a lot of outliers, i.e data points very far away from the mean. If there are, I use a Student's t instead. The Student's t distribution can be interpreted as a mixture of Gaussian with different variances, which is again very general.
In those examples, when I say visually, I mean that I use a Q-Q plot
Point 3, also deserves several book's chapters. The effects of using a distribution instead of another are limitless. So instead of going through it all, I will continue the two examples above.


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*In my early days, I did not know that Negative Binomial can have a meaningful interpretation so I used Poisson all the time (because I like to be able to interpret the parameters in human terms). Very often, when you use a Poisson, you fit the mean nicely, but you underestimate the variance. This means that you are unable to reproduce extreme values of your sample and you will consider such values as outliers (data points that do not have the same distribution as the other points) while they are actually not.

*Again in my early days, I did not know that Student's t also has a meaningful interpretation and I would use the Gaussian all the time. A similar thing happened. I would fit the mean and the variance well, but I would still not capture the outliers because almost all data points are supposed to be within 3 standard deviations of the mean. The same thing happened, I concluded that some points were "extraordinary", while actually they were not.
