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

Description

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

Usage

pareto2.ftest(x, y, s, alternative=c("two.sided", "less", "greater"),
    significance)

Arguments

a 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 samples $(X_1,...,X_n)$ i.i.d. $P2(k_x,s)$
and $(Y_1,...,Y_m)$ 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 the test statistic
T=n/m*sum(log(1+Y/m))/sum(log(1+X/n))
which, under $H_0$, has the Snedecor's F distribution with $(2m, 2n)$
degrees of freedom.
Note that for $k_x < k_y$, then $X$ dominates $Y$ stochastically.

`See Also`

dpareto2, pareto2.goftest, pareto2.htest