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=n/m*sum(log(1+Y/m))/sum(log(1+X/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`