psstat(x, n, cdf, kappa, ...)
ppareto2
.cdf
and pdf
.x
.cdf
) be a continuous c.d.f that is strictly increasing on $[a,b]$,
where $a=\inf{x: F(x)>0}$ and
$b=\sup{x: F(x)<1}$.< p="">Moreover, let
$\kappa:[0,1]\to[c,d]\subseteq[a,b]$
be any control function (parameter kappa
), i.e. a function that
is continuous and strictly increasing
and which fulfills $\kappa(0)=c$ and $\kappa(1)=d$.
The function computes the value of the c.d.f. of an S-statistic
w.r.t. to the control function for sample of size n
.
This result was given in (Gagolewski, Grzegorzewski, 2010).
Note that under certain conditions the distribution of an S-statistic
is asymptotically normal with expectation $\rho_\kappa$ (see rho.get
)
and variance $\rho_\kappa (1-\rho_\kappa)/n/(1+F(\kappa(\rho_\kappa)))^2$.
Sstat
, Sstat2
, dsstat
, rho.get