# Finding a suitable distribution for a data set of white noise

In the plot we see a mean zero process. It not entirely normally distributed. How can I find a suitable distribution for this process? It needs to be white noise and hence iid.

• "Normally distributed" is not a requirement of white noise.. What is your actual problem then? – whuber Nov 3 '17 at 21:14
• "suitable" for what purpose? How much will deviations matter, and of what kind? Do you actually need an explicit functional form, or is the purpose one for which an explicitly-written density is not necessary? – Glen_b Nov 4 '17 at 1:37

The shape of your histogram appears to be potentially Log-Normal with a negative shift. I would shift all of these values positively by $|min(x) + \epsilon|$ so that your support is non-negative, then overlay a log-normal density to see if it matches (where $\epsilon$ is some arbitrarily small number).
Here's a histogram of some random lognormal data that I shifted by $-1000$. It's probably close enough to what you need show my point that you should shift your observations into the positives and try to fit a distribution after that.
This is a an exponentiated random normal distribution with mean 1 and standard deviation 0.20 premultiplied by 400. Here's the R code I used:  x <- 400 * exp(rnorm(1000, mean = 1, sd = 0.20)) hist(x - 1000)