mult.mk.test {trend} | R Documentation |
Multivariate (Multisite) Mann-Kendall Test
Description
Performs a Multivariate (Multisite) Mann-Kendall test.
Usage
mult.mk.test(x, alternative = c("two.sided", "greater", "less"))
Arguments
x |
a time series object of class "ts" |
alternative |
the alternative hypothesis, defaults to |
Details
The Mann-Kendall scores are first computed for each variate (side) seperately.
with the signum function (see
sign
).
The variance - covariance matrix is computed according to Libiseller and Grimvall (2002).
with
and
Finally, the corrected z-statistics for the entire series
is calculated as follows, whereas a continuity correction is employed
for :
where
denotes the quantile of the normal distribution
is the vector of Mann-Kendall scores
for each variate (site)
and
denotes symmetric variance - covariance matrix.
Value
An object with class "htest"
data.name |
character string that denotes the input data |
p.value |
the p-value for the entire series |
statistic |
the z quantile of the standard normal distribution for the entire series |
null.value |
the null hypothesis |
estimates |
the estimates S and varS for the entire series |
alternative |
the alternative hypothesis |
method |
character string that denotes the test |
cov |
the variance - covariance matrix |
Note
Ties are not corrected. Current Version is for complete observations only.
References
Hipel, K.W. and McLeod, A.I. (1994), Time Series Modelling of Water Resources and Environmental Systems. New York: Elsevier Science.
Lettenmeier, D.P. (1988), Multivariate nonparametric tests for trend in water quality. Water Resources Bulletin 24, 505–512.
Libiseller, C. and Grimvall, A. (2002), Performance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71–84, doi:10.1002/env.507.
See Also
cor
,
cor.test
,
mk.test
,
smk.test
Examples
data(hcb)
mult.mk.test(hcb)