Re: [Gretl-devel] Q-Q plot, again
Allin Cottrell schrieb:
On Sat, 2 Jan 2010, Sven Schreiber wrote:
> Allin Cottrell schrieb:
>> I'm starting to implement the normal Q-Q plot as a built-in
>> command. Question: should we standardize the series to be plotted
>> against the normal?
>>
>> I notice that R does not standardize, but neither does it draw a
>> 45-degree line. If you don't standardize but do draw the
>> 45-degree line, then you get quite odd-looking results for a
>> series that has a substantially non-zero mean and/or a variance
>> that differs substantially from 1.
> I don't know what R does, but in general I'm afraid I don't quite
> understand the question; when you check whether a variable is normally
> distributed, it seems clear to me that of course you compare its
> empirical distribution to the closest member of the normal family/class.
> So you estimate mu and sigma. If that's what is meant, then sure go
> ahead and standardize...
There are two options here, which differ only in respect of what
values are shown on the axes: (1) convert the data to z-scores, or
(2) for the x-axis use quantiles of the normal distribution with
mean \hat{mu} and standard deviation \hat{sigma}. I'm not sure if
one of these is more "standard" than the other.
Neither am I, and both have their advantages. I guess I have a slight
preference for showing the "real units" (reflecting the empirical mu and
sigma) on the axis, but it's ultimately a matter of taste.
R does neither of these things: the command "qqnorm" plots the
"raw" quantiles of the data against the quantiles of N(0,1).
The advantage here is that the user can choose to compare against a
pre-specified mu and sigma by applying the appropriate transformation
beforehand. (The disadvantage of course is that the user always *must*
do some transformation manually.) As I was saying, I think it would be
useful to allow such an a-priori choice in gretl.
cheers,
sven