pareto2_test_f {agop} R Documentation

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

Description

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.

Usage

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 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.

Value

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.

Other Pareto2: pareto2_estimate_mle(), pareto2_estimate_mmse(), pareto2_test_ad(), rpareto2()
Other Tests: exp_test_ad(), pareto2_test_ad()