Watson's Test
Performs a Watson's goodness of fit test for the von Mises or circular uniform distribution.
watson.test(x, alpha=0, dist=c("uniform", "vonmises"))
## S3 method for class 'watson.test'
print(x, digits = 4, ...)x |
a vector. The object is coerced to class
|
alpha |
significance level of the test. Valid levels are 0.01, 0.05, 0.1. This argument may be ommited, in which case, a range for the p-value will be returned. |
dist |
distribution to test for. The default is the uniform
distribution. To test for the von Mises distribution, set |
digits |
integer indicating the precision to be used. |
... |
further arguments passed to or from other methods. |
If dist = "uniform", Watson's one-sample test for the circular uniform distribution is performed, and the results are printed. 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.
If dist = "vonmises", estimates of the population parameters are used to evaluate the von Mises distribution function at all data points, thereby arriving at a sample of approximately uniformly distributed data, if the original observations have a von Mises distribution. The one-sample Watson test is then applied to the transformed data as above.
a list with the statistic, alpha, the number of observations, the
distribution and 'row' which is used by print.watson.test to
evaluate the p-value.
Claudio Agostinelli and Ulric Lund
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.
# Generate data from the uniform distribution on the circle. x <- circular(runif(100, 0, 2*pi)) watson.test(x) # Generate data from a von Mises distribution. x <- rvonmises(n=50, mu=circular(0), kappa=4) watson.test(x, alpha=0.05, dist="vonmises")
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