pareto2.htest: Two-sample h-test for equality of shape parameters for Type II-Pareto distributions with known common scale parameter

Description

Performs $h$-test for equality of shape parameters of two samples from the Pareto type-II distributions with known and equal scale parameters, $s>0$.

Usage

pareto2.htest(x, y, s, alternative=c("two.sided", "less", "greater"),
    significance=0.05, wyg, verbose=TRUE, drho=0.005, K, improve=TRUE)

Arguments

an n-element non-negative numeric vector of data values.

scale parameter, $s>0$.

alternative

indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater".

significance

significance level. See Value for details.

wyg

precomputed h-dependent acceptation region or NULL. See Value for details.

verbose

logical; if TRUE then the computation progress will be printed out.

drho

power calculation accuracy, a single number in [0.001, 0.1]. The smaller the value the slower computation, but more precise. This is used to determine K iff K is not given.

numeric vector; shape parameters for which to calculate the power function or NULL.

improve

logical; if TRUE then the greedy heuristic algorithm for improving the acceptation region will be run.

Value

The list of class power.htest with the following components is passed as a result: ll{ statistic the value of the test statistic. result either FALSE (accept null hypothesis) or TRUE (reject). alternative a character string describing the alternative hypothesis. method a character string indicating what type of test was performed. data.name a character string giving the name(s) of the data. wyg a numeric vector giving the h-dependent acceptation region used. size size of the test corresponding to wyg. qual quality of the test corresponding to wyg, the closer to significance, the better. } Currently no method for determining the p-value of this test is implemented.

Details

Given two equal-sized samples $X=(X_1,...,X_n)$ i.i.d. $P2(k_x,s)$ and $Y=(Y_1,...,Y_m)$ i.i.d. $P2(k_y,s)$ this test verifies the null hypothesis $H_0: k_x=k_y$ against two-sided or one-sided alternatives, depending on the value of alternative. It bases on test statistic T=H(Y)-H(X) where $H$ denotes Hirsch's $h$-index (see index.h).

Note that for $k_x < k_y$, then $X$ dominates $Y$ stochastically.

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.