I have a number of data sets each containing the measurement of all trees diameter within one hectare.
A Weibull function distribution is fitted to the data and for each data set I obtain the parameters shape and scale and the standard deviation for each parameter.
How can I compare the shape and scale parameters to determine which of these distributions are statistically different, in other words the distribution of tree diameters is different? All distributions are non-normal and the data sets are independent from each other. I do not have confidence interval.
Can I say that two distributions are different if the standard deviation from one distribution does not overlap with the shape and scale parameters from the other distribution? Or should the standard deviations from both distribution not overlap? Or is there some formal statistical test to be done?