micro@ Are there any "CONTINUOUS" distributions with variance proportional to the mean, within the exponential dispersion family, or at least within the exponential family? Thanks,
micro@ I have a dataset whose variance looks "proportional", but not "equal", to the expectation. That's why I want to find such a distribution, such that I can try generalized linear models on the data. For example, the Gamma distribution would have variance proportional to squared mean, whereas inverse Gaussian would have variance proportional to cubed mean. I want a distribution with variance proportional to the mean itself.
micro@ Thanks a lot. It indeed satisfies the question I asked. But I don't know whether this will solve my analysis problem or not. 2 is a constant, not a parameter, for Chi-square, which is somewhat too stringent for modelling purposes. The data I have do showed a proportionality between mean and variance, but the dispersion parameter is not 2. Is there any over-dispersion version of Chi-squre GLM? Also, I'm confused with Chi-square and Gamma. Chi-square is a special case of Gamma, but the variance function for Gamma is a quadratic function, hence not the linear proportionality showed in data. Where does the paradox come from?
