pvaldistance {bootruin} R Documentation

## Distance Measures of Empirical Probability Functions

### 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

```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 Cramér-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.

### Examples

```# 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")
```

[Package bootruin version 1.2-4 Index]