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

Description

Performs asymptotic (approximate) $h$-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.approx(x, y, s, alternative=c("two.sided", "less",
    "greater"), significance)

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, $0<$significance$<1$ or="" NULL. See Value for details.

`Value`

If significance is not NULL, then
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.
}
Otherwise, the list of class htest with the following components is passed as a result:
ll{
statistic 	the value of the test statistic.
p.value 	the p-value of the test.
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.
}

`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 a test statistic that is a function of {H(Y)-H(X)},
where $H$ denotes Hirsch's $h$-index (see index.h).
This statistic approximately has asymptotically standardized normal distribution under $H_0$.
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.

`See Also`

dpareto2, pareto2.goftest, pareto2.ftest, pareto2.htest, index.h