trend (version 0.2.0)

partial.mk.test: Partial Mann-Kendall Test

Description

Performs a partial Mann-Kendall test

Usage

partial.mk.test(x, z)

Arguments

x

a "vector" or "ts" object that contains the variable, which is tested for trend (i.e. correlated with time)

z

a "vector" or "ts" object that contains the variable, which effect on "x" is partialled out

Value

An object of class "htest"

method

a character string indicating the chosen test

data.name

a character string giving the name(s) of the data

statistic

the value of the test statistic

estimate

the Mann-Kendall score S and the variance varS

alternative

a character string describing the alternative hypothesis

p.value

the p-value of the test

Warning

Current Version is for complete observations only. The "method=='Partial'" is in testing mode.

Details

According to Libiseller and Grimvall (2002), the expected value for the Mann-Kendall Score of variable "a" that is correlated with the covariate "b" is: \(E = S_b * \sigma_{ab} / \sigma_{bb}\)

Furthermore, the expected variance of "a" is: \(Var = \sigma_{aa} - \sigma_{ab} / \sigma_{bb} * \sigma_{ba}\)

Finally, the Z-Quantile is defined as: \(Z = (S_a - E) / \sqrt(Var)\)

References

Libiseller, C. and Grimvall, A., (2002). Performance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71-84, http://dx.doi.org/10.1002/env.507.

See Also

partial.cor.trend.test, summary.trend.test

Examples

# NOT RUN {
data(maxau)
s <- maxau[,"s"]; Q <- maxau[,"Q"]
partial.mk.test(s,Q)
# }