pareto2.confint.h: Two-sided exact confidence interval for the theoretical h-index
Description
Computes the exact two-sided confidence interval for the theoretical $h$-index
of a probability distribution in an $(X_1,\dots,X_n)$ i.i.d. Pareto-type II
model with known scale parameter $s>0$.Usage
pareto2.confint.h(h, s, n, conf.level=0.95, tol=1e-12)
Arguments
h
observed value of the $h$-index
conf.level
confidence level; defaults 0.95.
tol
the desired accuracy (convergence tolerance).
Value
- Vector of length 2 with the computed bounds of the confidence interval.
Details
The Theoretical $h$-index for a sequence of $n$ i.i.d. random variables
with common increasing and continuous c.d.f. $F$ defined on $[0,\infty)$
is equal to $n\varrho_\kappa$, where $\rho_\kappa$
is the $\rho$-index of $F$ for $\kappa(x)=nx$, see rho.get
for details.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.