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.