rpteststat: Computation of the Test Statistic for the Probability of Ruin In bootruin: A Bootstrap Test for the Probability of Ruin in the Classical Risk Process

Description

This function computes the test statistic for the test of the probability of ruin

Usage

 `1` ```rpteststat(x, x.null, se) ```

Arguments

 `x` The observed/estimated probability of ruin `x.null` The null probability of ruin `se` The standard error of `x`

Details

This function studentizes (i.e., centers and rescales) the observed probabilities of ruin in a way that they can be further processed by `rppvalue`. This latter computes p-values for the test with the null hypothesis that the probability of ruin is equal to `x.null` versus the one-sided alternative that probability of ruin is smaller than `x.null`

There are two possible scenarios how to use this function:

The first one is to compute the test statistic for vector of estimated probabilities of ruin (where each element corresponds to an independent sample of observed claims) using a pre-determined value of `x.null`. In this case the output is a matrix with `length(x)` columns and `length(x.null)` rows.

The second use is to compute the bootstrap replications of the test statistic. In that case the estimated probabilities of ruin are used for `x.null`, and the numbers of rows of `x` has to match the length of `x.null`, i.e. there is one row of bootstrap replications of the probability of ruin for each sample of claim sizes.

Value

A numeric matrix that contains the test statistic. Its dimension depends on the input, see Details.

Note

The dimensions (or lengths) of `x` and `se` have to be the same.

See `ruinprob` on how to obtain the estimators of the probabilities of ruin, `rpjack` on how to get approximate standard errors of the former, and `rppvalue` on how to compute the p-values of the test described here.