Performes the Buishand range test for change-point detection of a normal variate.
br.test(x, m = 20000)A list with class "htest" and "cptest"
character string that denotes the input data
the p-value
the test statistic
the null hypothesis
the time of the probable change point
the alternative hypothesis
character string that denotes the test
numeric vector of Sk for plotting
a vector of class "numeric" or a time series object of class "ts"
numeric, number of Monte-Carlo replicates, defaults to 20000
Let \(X\) denote a normal random variate, then the following model with a single shift (change-point) can be proposed:
$$ x_i = \left\{ \begin{array}{lcl} \mu + \epsilon_i, & \qquad & i = 1, \ldots, m \\ \mu + \Delta + \epsilon_i & \qquad & i = m + 1, \ldots, n \\ \end{array} \right.$$
with \(\epsilon \approx N(0,\sigma)\). The null hypothesis \(\Delta = 0\) is tested against the alternative \(\Delta \ne 0\).
In the Buishand range test, the rescaled adjusted partial sums are calculated as
$$S_k = \sum_{i=1}^k \left(x_i - \hat{x}\right) \qquad (1 \le i \le n)$$
The test statistic is calculated as: $$Rb = \left(\max S_k - \min S_k\right) / \sigma$$.
The p.value is estimated with a Monte Carlo simulation
using m replicates.
Critical values based on \(m = 19999\) Monte Carlo simulations are tabulated for \(Rb / \sqrt{n}\) by Buishand (1982).
T. A. Buishand (1982), Some Methods for Testing the Homogeneity of Rainfall Records, Journal of Hydrology 58, 11--27.
G. Verstraeten, J. Poesen, G. Demaree, C. Salles (2006), Long-term (105 years) variability in rain erosivity as derived from 10-min rainfall depth data for Ukkel (Brussels, Belgium): Implications for assessing soil erosion rates. Journal of Geophysical Research 111, D22109.
efp
sctest.efp
data(Nile)
(out <- br.test(Nile))
plot(out)
data(PagesData) ; br.test(PagesData)
Run the code above in your browser using DataLab