R: Kuiper's Test

kuiper.test {circular} | R Documentation

## Kuiper's Test

### Description

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

### Usage

    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.

### See Also

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

### Examples

    # 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)

[Package circular version 0.4-93 Index]