CITAN (version 2011.03-2)

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

s

scale parameter, $s>0$.

n

sample size.

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.

See Also

index.h, ppareto2, rho.get, pareto2.confint.rho, pareto2.confint.h.upper, pareto2.confint.h.upper