If I obtain a histogram of physical observations, can I compute summary statistics without making a restrictive assumption the functional form of the PDF? For example (but not restricted to this case) if I have an observed distribution that is bimodal: how can I obtain numerical measurements of moments such as standard deviation (variance), skewness, and kurtosis?
My experiments vary through time, I need to be able to make a meaningful time series comparisons about the distributions in rolling windows. Are there "model-free" approaches to these measurements, or can I assume sub-normal distributions to get some valuable statistics? Any references are much appreciated.
Try fitting a mixture of normal distributions to these data, e.g., using the mclust software in R. A mixture of two normals should fit well.