pareto2_test_f: Two-Sample F-test For Equality of Shape Parameters for Type II-Pareto Distributions

Description

Performs F-test for equality of shape parameters of two samples from the Pareto type-II distributions with known and equal scale parameters, $s>0$.

Usage

pareto2_test_f(x, y, s,
    alternative = c("two.sided", "less", "greater"),
    significance = NULL)

Arguments

a non-negative numeric vector

the known 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
  the Value section for details

`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: 
statisticthe value of the test statistic.
p.valuethe p-value of the test.
alternativea character string describing the
  alternative hypothesis.
methoda character
  string indicating what type of test was performed.
data.namea 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 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.

`See Also`

Other Pareto2: dpareto2,
  pareto2_estimate_mle,
  pareto2_estimate_mmse,
  ppareto2, qpareto2,
  rpareto2