# kuiper.test: Kuiper's Test In circular: Circular Statistics

## Description

Performs Kuiper's one-sample test of uniformity on the circle.

## Usage

 ```1 2 3``` ```kuiper.test(x, alpha=0) ## S3 method for class 'kuiper.test' print(x, digits = 4, ...) ```

## Arguments

 `x` a vector. The object is coerced to class `circular`. `alpha` significance level of the test. Possible levels are 0.15, 0.1, 0.05, 0.025, 0.01. Alpha may be omitted or set to zero, in which case a range for the p-value of the test will be printed. `digits` integer indicating the precision to be used. `...` further arguments passed to or from other methods.

## Details

Kuiper's test statistic is a rotation-invariant Kolmogorov-type test statistic. The critical values of a modified Kuiper's test statistic are used according to the tabulation given in Stephens (1970).

## Value

A list with the statistic and alpha value.

## Note

Kuiper's one-sample test of uniformity is performed, and the results are printed to the screen. If alpha is specified and non-zero, the test statistic is printed along with the critical value and decision. If alpha is omitted, the test statistic is printed and a range for the p-value of the test is given.

## Author(s)

Claudio Agostinelli and Ulric Lund

## References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 7.2, World Scientific Press, Singapore.

Stephens, M. (1970). Use of the Kolmogorov-Smirnov, Cramer-von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society, B32, 115-122.

`range.circular`, `rao.spacing.test`, `rayleigh.test` and `watson.test`

## Examples

 ```1 2 3 4 5 6``` ```# Generate data from the uniform distribution on the circle. data <- circular(runif(100, 0, 2*pi)) kuiper.test(data) # Generate data from the von Mises distribution. data <- rvonmises(n=100, mu=circular(0), kappa=3) kuiper.test(data, alpha=0.01) ```

### Example output

```Attaching package: 'circular'

The following objects are masked from 'package:stats':

sd, var

Kuiper's Test of Uniformity

Test Statistic:  1.5174
P-value > 0.15

Kuiper's Test of Uniformity

Test Statistic:  6.131
Level 0.01 Critical Value: 2.001
Reject Null Hypothesis

```

circular documentation built on May 1, 2019, 7:57 p.m.