Performs the F-test for the equality of shape parameters of two samples from 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
)If significance is not NULL, then
the list of class power.htest with the following components is yield in 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 yield in 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.
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
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 is based on the 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 \(H_0\), follows 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()