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

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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

1
2
pareto2_test_f(x, y, s, alternative = c("two.sided", "less", "greater"),
  significance = NULL)

Arguments

x

a non-negative numeric vector

y

a non-negative numeric vector

s

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

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=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 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.

See Also

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