Question

First, I should specify that my knowledge of statistics is fairly limited, so please forgive me if my question seems trivial or perhaps doesn’t even make sense.

I have data that doesn’t appear to be normally distributed. Typically, when I plot confidence intervals, I would use the mean +- 2 standard deviations, but I don’t think that is acceptible for a non-uniform distribution. My sample size is currently set to 1000 samples, which would seem like enough to determine if it was a normal distribution or not.

I use Matlab for all my processing, so are there any functions in Matlab that would make it easy to calculate the confidence intervals (say 95%)?

I know there are the ‘quantile’ and ‘prctile’ functions, but I’m not sure if that’s what I need to use. The function ‘mle’ also returns confidence intervals for normally distributed data, although you can also supply your own pdf.

Could I use ksdensity to create a pdf for my data, then feed that pdf into the mle function to give me confidence intervals?

Also, how would I go about determining if my data is normally distributed. I mean I can currently tell just by looking at the histogram or pdf from ksdensity, but is there a way to quantitatively measure it?

Thanks!

Answer 1

Are you sure you need confidence intervals or just the 90% range of the random data?

If you need the latter, I suggest you use prctile(). For example, if you have a vector holding independent identically distributed samples of random variables, you can get some useful information by running

y = prcntile(x, [5 50 95])

This will return in [y(1), y(3)] the range where 90% of your samples occur. And in y(2) you get the median of the sample.

Try the following example (using a normally distributed variable):

t = 0:99;
tt = repmat(t, 1000, 1);
x = randn(1000, 100) .* tt + tt;  % simple gaussian model with varying mean and variance
y = prctile(x, [5 50 95]);

plot(t,  y);
legend('5%','50%','95%')