pareto2_test_f {agop}  R Documentation 
Performs the Ftest for the equality of shape parameters
of two samples from Pareto typeII distributions with known
and equal scale parameters, s>0
.
pareto2_test_f(
x,
y,
s,
alternative = c("two.sided", "less", "greater"),
significance = NULL
)
x 
a nonnegative numeric vector 
y 
a nonnegative numeric vector 
s 
the known scale parameter, 
alternative 
indicates the alternative hypothesis and must be one of

significance 
significance level, 
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 twosided or onesided 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.
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 pvalue 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.
Other Pareto2:
pareto2_estimate_mle()
,
pareto2_estimate_mmse()
,
pareto2_test_ad()
,
rpareto2()
Other Tests:
exp_test_ad()
,
pareto2_test_ad()