Performs F-test for equality of shape parameters of two samples from the Pareto type-II distributions with known and equal scale parameters, \(s>0\).
pareto2_test_f(x, y, s, alternative = c("two.sided", "less", "greater"),
significance = NULL)a non-negative numeric vector
a non-negative numeric vector
the known scale parameter, \(s>0\)
indicates the alternative hypothesis and must be one of
"two.sided" (default), "less", or "greater"
significance level, \(0<\)significance\(<1\)
or NULL. See the Value section for details
If significance is not NULL, then
the list of class power.htest with the following components is passed as a result:
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:
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.
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 test statistic
\(T(X,Y)=\frac{n\sum_{i=1}^m\log(1+Y_i/m)}{m\sum_{i=1}^n\log(1+X_i/n)}\)
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.
Other Pareto2: pareto2_estimate_mle,
pareto2_estimate_mmse,
pareto2_test_ad, rpareto2
Other Tests: exp_test_ad,
pareto2_test_ad