rkt (version 1.8)

rkt-package: Mann-Kendall Test, Seasonal and Regional Kendall Tests

Description

Contains function rkt which computes the Mann-Kendall test (MK) and the Seasonal and the Regional Kendall Tests for trend (SKT and RKT) and Theil-Sen's slope estimator.

Author

Maintainer: Aldo Marchetto <[e-mail]>

Details

Package:	rkt
Type:	Package
Version:	1.7
Date:	2026-08-25
License:	GPL-2

This function computes the Mann-Kendall test (MK) and the Seasonal and the Regional Kendall Tests for trend (SKT and RKT) and Sen's slope estimator.
MK, SKT and RKT are tests for monotonic trend in time series based on the Kendall rank correlation.
SKT and RKT are intrablock tests in which test statistics are computed for each season or month (SKT) or for each site (RKT) and combined in an overall test.
In RKT, seasonality can be accounted for by using a blocking variable combining both sites and seasons, such as (site * 12 + month).
When a covariable is defined, this function also computes partial RKT and SKT.
To allow for non-regular sampling dates, input data should be vectors, not time series.
If there are no block definition nor ties, exact probability can be optionally calculatesd by recurrence relation.

References

Helsel D.R., Frans L.M. 2006 The regional Kendall test for trend: Environmental Science and Technology 40, 4066--4073

Helsel D.R., Mueller D.K., Slack J.R. 2006 Computer program for the Kendall family of trend tests U.S. Geological Survey Scientific Investigations Report 2005-5275, 4 pp.

Hirsch R.M., Slack J.R., Smith R.A. Techniques of trend ananlyis for monthly water quality data. Water Resources Research 18, 107-121

Hirsch R.M., Slack J.R. 1984 A nonparametric test for seasonal data with serial dependance. Water Resources Research 20, 727-732

Libiseller C., Grimvall A. 2002 Perfomance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71-84

Mann H.B. 1945. Nonparametric tests against trend. Econometrica 13, 245-249

Kaarsemaker L., Wijngaarden A. van 1953 Tables for use in rank correlation. Report R73 of the Computation Depattment of the Mathematical Centre, Amsterdam

Best, D.J., Gipps, P.G. 1974 Algorithm AS 71: The Upper Tail Probabilities of Kendall's Tau. Journal of the Royal Statistical Society. Series C (Applied Statistics), 23: 98-100

Marchetto A., Rogora M., Arisci S. 2013 Trend analysis of atmospheric deposition data: a comparison of statistical approaches. Atmospheric Environment 64, 95-102

Examples

#
# monthly data, using covariate and intra-block correction
#
data(pie1)
ex<-rkt(pie1$Year,pie1$SO4,pie1$Month,pie1$mm,TRUE)
print(ex)
#
# weekly data, no intrablock correction
#
data(pie1w)
ex<-rkt(pie1w$Date,pie1w$SO4)
print(ex)
#
# monthly data, hydrological years (oct-sep) as in USGS program
#
data(pie1)
ex<-rkt(pie1$Year+floor(pie1$Month/10),pie1$SO4,pie1$Month,,TRUE)
print(ex)
#