CITAN (version 2011.08-1)

dsstat: Distribution of S-statistics - density

Description

Computes the density function of the S-statistic w.r.t. to a control function in an i.i.d. model with common increasing and continuous c.d.f. $F$ defined on $[0,\infty)$.

Usage

dsstat(x, n, cdf, pdf, kappa, kappaInvDer, ...)

Arguments

x

numeric vector.

n

sample size.

cdf

a cumulative distribution function $F$, e.g. ppareto2.

pdf

a density function $F'$, e.g. dpareto2.

kappa

an increasing function, $\kappa$, a so-called control function.

kappaInvDer

the derivative of the inverse of $\kappa$.

...

optional arguments to cdf and pdf.

Value

• The value of the density at x.

Details

The function computes the value of the p.d.f. of an S-statistic w.r.t. to the control function kappa for sample of size n. Note that the result is valid only at continuity points of $F'$.

For more information see man page on psstat and the paper (Gagolewski, Grzegorzewski, 2010).

References

Gagolewski M., Grzegorzewski P., S-Statistics and Their Basic Properties, In: Borgelt C. et al (Eds.), Combining Soft Computing and Statistical Methods in Data Analysis, Springer-Verlag, 2010, 281-288.

See Also

Sstat, Sstat2, psstat, rho.get