# How can I compare distributions using only mean and standard deviation?

I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built from very similar samples. I'm looking for a mechanism to detect when the distributions deviate from one another by some threshold. Access to historical observations is limited.

• Are you asking how to determine which distributions the data follow based on the mean and standard deviation? Oct 31, 2011 at 23:34

## 2 Answers

There are a number of different tests that are generally used to compare samples to different distributions, such as Jarque-Bera, Anderson-Darling, and Kolmogorov–Smirnov (see this related question).

In your case, with just the standard deviation and mean, there isn't a whole lot to say. You need to assume a distribution (e.g. normal). You would be able to tell much more if you could at least get the skewness and kurtosis.

Be careful, remember that the mean and the standard deviation don't tell you the whole story: http://en.wikipedia.org/wiki/Anscombe%27s_quartet