I am en experimentalist and in most of my experiments I am interested in measuring the properties of distributions, i.e. the phenomenon I am measuring is stochastic and the parameters I am interested in are (in the simplest case) say the mean value and the width of the distribution (variance of standard distribution). My "in" data is a times series wth n samples sampled at some frequency fs which is then post-processed in Matlab. If often deal with quite long time-series (millions of points) that take hours or days to aquire, and I am therefore interested in understanding how much here really is to gain my say doubling the number of aquired points. My question is a practical one: how many samples do I need in order to estimate the shape of the distribution? I know that the accuracy by which I can estimate the mean improves as √n, at least if one assumes a normal distribution. But how quickly does the estimate of the std improve? Also, can one say something about many samples one need to estimate the parameters for other common distributions (Poissonian etc)?