TwoSample Ftest For Equality of Shape Parameters for Type IIPareto Distributions
Description
Performs Ftest for equality of shape parameters of two samples from the Pareto typeII distributions with known and equal scale parameters, s>0.
Usage
1 2  pareto2_test_f(x, y, s, alternative = c("two.sided", "less", "greater"),
significance = NULL)

Arguments
x 
a nonnegative numeric vector 
y 
a nonnegative numeric vector 
s 
the known scale parameter, s>0 
alternative 
indicates the alternative hypothesis and must be one of

significance 
significance level, 0< 
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 twosided or onesided alternatives, depending
on the value of alternative
.
It bases on 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.
Value
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 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.
See Also
Other Pareto2: dpareto2
,
ppareto2
, qpareto2
,
rpareto2
;
pareto2_estimate_mle
;
pareto2_estimate_mmse