Testing the Homogeneity and Sufficiency of empirical data

Hello,

In order to be able to use statistical tools to calculate reserves for a Professional Indemnity and a Medmal book, my state insurance department requires that I prove that the data that I´m using is Homogeneous and Sufficient for statistical analysis.

¿Any ideas on which methods I can use to test this?

For Homogeneity, I´ve read that histograms are used: you construct a histogram, and if the resulting distribution is unimodal, then your sample is homogeneous. Of course, it will depend a lot on which brackets you use on your histogram, and it´s a little bit judgmental, not like a test of hypothesis which will tell you with x% of confidence that you don´t reject the null hypothesis... Any suggestions? Any alternative method?

For Sufficiency, I found a paper stating that your mimimum sample size for estimating the mean within d% of error with a% confidence level is:
[(Za/2)^2 CV^2] / d^2
Za/2: the standardized Z value for a/2%
CV : sample coefficient of variation
Does this still make sense for the purposes I'm using it? Does this work with any distribution, or it has to be a normal? Can I fit a lognormal distribution to my empirical data, and after a positive test of hypothesis that it fits the curve, apply it to the log of my empirical data?

Any help would be much appreciated. Thanks.
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