# pvaldistance: Distance Measures of Empirical Probability Functions In bootruin: A Bootstrap Test for the Probability of Ruin in the Classical Risk Process

## Description

This function provides a framework to evaluate various measures of distance between an empirical distribution (induced by the dataset provided) and a theoretical probability distribution.

## Usage

 `1` ```pvaldistance(x, method = c("ks", "cvm"), dist.to = c("uniform")) ```

## Arguments

 `x` a numeric vector containing a data sample. `method` a character string indicating which measure of distance is computed. `dist.to` a character string determining the (theoretical) probability distribution that is used as a reference.

## Details

`method = "ks"` gives the Kolmogorov-Smirnov distance.

`method = "cvm"` yields the CramÃ©r-von-Mises criterion (scaled with the sample size).

## Value

A positive real number giving the distance measure.

## Note

At the moment, `dist.to = "uniform"` (the uniform distribution on the unit interval) is the only valid option for the theoretical distribution, and hence the members of `x` have to lie in the unit interval.

See `ks.test` for the Kolmogorov-Smirnov test.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# A sample from the standard uniform distribution x <- runif(100, 0, 1) # Distance to uniformity should be small pvaldistance(x, "ks") pvaldistance(x, "cvm") # A sample from the Beta(2, 7) distribution y <- rbeta(100, 2, 7) # Distance to uniformity should be much larger here pvaldistance(y, "ks") pvaldistance(y, "cvm") ```