Expected values and variances of chi+sups(2) distributions are directly
related (cf. url(this link)
(https://en.wikipedia.org/wiki/Variance#Distribution_of_the_sample_variance)):
Their expected values are equal to the population variance (= tt(var)), and
their variances are equal to
        verb(
    2 * sqr(var) / (N - 1)
        )
    where tt(N) represents the sample size.

In tt(simrisc) the used chi+sups(2) distribution is computed from the
population variance as specified in the configuration file (like 21.1 for the
tt(Normal) carrier's standard deviation) and the number of simulated cases
(like 100,000). In that case the variance of the variances of such
samples equals
        verb(
    2 * sqr(21.1) / (100,000 - 1) = 0.0089
        )
    (and std. dev. 0.0944)

Using tt(sd) to represent the standard deviation drawn from a distribution of
standard deviations using samples of size tt(N) and population standard
deviation tt(sigma), then
        verb(
    (N - 1) * sqr(sd) / sqr(sigma)
        )
    follows a chi+sups(2) distribution with tt(N - 1) degrees of freedom.
Using tt(chi^2[df]) to represent such a distribution,  we get
        verb(
    (N - 1) * sqr(sd) / sqr(sigma): distributed as chi^2[N - 1]
        )

From sigma, N and a random value drawn from tt(chi^2[N - 1]) a corresponding
tt(sd) value can now be computed:
        verb(
    sd = sqrt( sqr(sigma) * chi^2[N - 1] / (N - 1) )
        )

The following table illustrates what these tt(sd) values might look like when
computed 10 times: (using N = 100,000) en sigma = 21.2):
        verb(
    ----------------------
          chi^2       sd
    ----------------------
     1: 100805.0 -> 21.285
     1:  99499.8 -> 21.147
     2:  99867.1 -> 21.186
     3:  99873.8 -> 21.187
     4: 100076.0 -> 21.208
     5:  99895.8 -> 21.189
     6:  99952.9 -> 21.195
     7: 100558.0 -> 21.259
     8: 100126.0 -> 21.213
    10:  99289.8 -> 21.125
    ----------------------
        )

The procedure described here is used to compute spread variations for standard
deviations.
