🚀 go-pugleaf

> OK, I believe you can have F and Chi-sq for fractional dfs.
>
> But can anyone give a good intuitive explanation of what a
fractional
> df might be, in practice? "Well, let's enter another half
parameter
> here!?"
>
> Brendan Halpin
> Dept of Applied Social Studies
> University of Oxford
>
>

OK, I'll give you my example and you judge whether it makes sense
or not.

I just used the gamma distribution to simulate changes in the
distribution of systolic blood pressure in the population over
time. Upon trying different gamma distributions it turned out that
the chi square distribution with a couple of degrees of freedom
looked quite similar to my initial observed distribution of SBP. By
reducing the df's by a small fraction each year I achieve changes
which make substantive sense: If I assume that the population grows
healthier over time I want to produce a gradual decrease of the
right skew while the minimum value stays put (i.e. I reduce the
proportion high, allegedly unhealthy, SBP's).

Hence, here I don't regard the parameter of the distribution as the
number of free parameters in a model. I use it for other purposes
where the possibility to define the chi square distribution for a
non-integer mean comes in very handy.


Magnus Stenbeck
Center for Epidemiology
National Board of Health & Welfare
Sweden