So I plotted all price rises and falls of a certain product over

>>8454463
Here's what you do to find out:

1. You fit the gaussian pdf
2. You calculate the cumulative distribution of your data
3. You calculate your fitted cdf
4. You calculate the maximum difference between fit and data
5. What you just did is called the Kolmogorov-Smirnov test. You can look it up somewhere to find thresholds for specific confidence levels.

You should calculate errors to your data too. It should be pretty simple to do (you count shit and sort them into bins, so it's poisson statistic). If you've managed to do that, you can also do a chi-squared test:

1. You fit the gaussian pdf
2. For every bin you calculate [eqn] \sum_i \frac{x_i^\mathrm{fit} - x_i^\mathrm{data}}{\sigma_i}[/eqn]
3. You can look up thresholds etc online

Now, from the image, it's impossible to tell, because you didn't give us your statistics (most importantly, how many samples you have), you only gave us a density estimate, which is useless for this kind of stuff (really, try to avoid density estimation). It has this strange peak that makes the whole thing look like the superposition of two gaussians (one with high sigma, one with low sigma), but that's just a guess.

>>8454502
question for you since you obviously know your stats (not OP)

I was in a situation a while ago where I wanted to compare two sample sets to see if they were from the same distribution (i'm a biologist who knows just enough stats to hurt myself), and after some digging came across K-S and other related tests. I also came across some people saying things along the lines of, "tests for normality can be done, sure, but are rarely worth doing". their reasoning was something like, no comparison of empirical data is going to find exactly the same distribution anyway, and what matters is what level of difference you're willing to tolerate before you say they're meaningfully different

what are your thoughts on that?

>>8454463
>Is this a normal distribution
No, it looks like a normal (Gaussian) distro
with a superimposed (additional) triangular distro.

>>8454527
Just to add to this, I'm an Ecologist, need stats to get by but obviously not an expert. Most people test for normality simply to say ok, it's non normal so I'll use non parametric tests or whatever. But like you said, it's meaningless particularly for bio/eco data. I don't have an answer to your question but yes you will find a lot of discussion regarding this question, and the answer will always change depending on your particular dataset (sample size things like that). Normality can inform you but it isnt the be-all-end-all

thanks for the answers guys