# rayleigh.test: Rayleigh Test of Uniformity In circular: Circular Statistics

## Description

Performs a Rayleigh test of uniformity, assessing the significance of the mean resultant length. The alternative hypothesis is a unimodal distribution with unknown mean direction and unknown mean resultant length if `mu` is `NULL` otherwise the alternative hypothesis is a unimodal distribution with a specified mean direction and unknown mean resultant length.

## Usage

 ```1 2 3``` ```rayleigh.test(x, mu = NULL) ## S3 method for class 'rayleigh.test' print(x, digits=4, ...) ```

## Arguments

 `x` a vector. The object is coerced to class `circular`. `mu` Specified mean direction in alternative hypothesis as a `circular` object. `digits` integer indicating the precision to be used. `...` further arguments passed to or from other methods.

## Value

Returns a list with three components: the mean resultant length, `statistic`, the p-value of the test statistic, `p.value` and the value of the alternative mean direction `mu`.

## Author(s)

Claudio Agostinelli and Ulric Lund

## References

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Sections 3.3.2 and 3.4.1, World Scientific Press, Singapore.

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

## Examples

 ```1 2 3 4 5``` ```x <- rvonmises(n=25, mu=circular(pi), kappa=2) # General alternative rayleigh.test(x) # Specified alternative rayleigh.test(x, mu=circular(0)) ```

### Example output

```Attaching package: 'circular'

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

sd, var

Rayleigh Test of Uniformity
General Unimodal Alternative

Test Statistic:  0.5242
P-value:  7e-04

Rayleigh Test of Uniformity
Alternative with Specified Mean Direction:  0

Test Statistic:  -0.5217
P-value:  0.9999
```

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