[GRASS-dev] Re: [GRASS-user] Re: Calculating standard error of many maps?

[Glynn Clements]

Hamish wrote:

> > I can add sum of squares/cubes/etc to r.series easily
> > enough if there is a use for them.
> 
> well, sum of squares is useful so you can calculate variance & friends.
> don't know of any use for cubes+.

Skew needs sum(x^3), kurtosis needs sum(x^4).

> r.univar/stats.c:
>     /* all these calculations get promoted to doubles, so any DIV0 becomes nan */
>     mean = stats->sum / stats->n;
>     variance = (stats->sumsq - stats->sum * stats->sum / stats->n) / stats->n;
>     if (variance < GRASS_EPSILON)
>         variance = 0.0;
>     stdev = sqrt(variance);
>     var_coef = (stdev / mean) * 100.;   /* perhaps stdev/fabs(mean) ? */
> 
> 
> adding sum of sq would let people calc that with r.series+r.mapcalc
> manually.
> 
> not sure what components are required to calc kurtosis & skewness,
> although I've an idea that they'd be possible with a single-serial-pass
> construction method as s.cellstats had them (??).

Like variance, it's possible to calculate them in a single pass
(v.univar does so), but the inaccuracies of a single-pass calculation
will get worse with higher powers.

-- 
Glynn Clements <glynn at gclements.plus.com>