p.chisq.test {RecordTest} | R Documentation |
Pearson's Chi-Square Test for Probabilities of Record
Description
This function performs a chi-square goodness-of-fit test
based on the record probabiliteis p_t
to study the hypothesis
of the classical record model (i.e., of IID continuous RVs).
Usage
p.chisq.test(
X,
record = c("upper", "lower"),
simulate.p.value = FALSE,
B = 1000
)
Arguments
X |
A numeric vector, matrix (or data frame). |
record |
A character string indicating the type of record to be calculated, "upper" or "lower". |
simulate.p.value |
Logical. Indicates whether to compute p-values by Monte Carlo simulation. It is recommended if the function returns a warning (see Details). |
B |
If |
Details
The null hypothesis of this chi-square test is that in every vector
(columns of the matrix X
), the probability of record at
time t
is 1/t
as in the classical record model,
and the alternative that the probabilities are not equal to those values.
First, the chi-square goodness-of-fit statistics to study the null
hypothesis H_0:\,p_t = 1/t
are calculated for each time
t=2,\ldots,T
, where the observed value is the number of records at
time t
in the M
vectors and the expected value under the null
is M / t
. The test statistic is the sum of the previous T-1
statistics and its distribution under the null
is approximately \chi^2_{T-1}
.
The chi-square approximation may not be valid with low M
, since it
requires expected values > 5
or up to 20\%
of the expected
values are between 1 and 5. If this condition is not satisfied, a warning
is displayed. In order to avoid this problem, a simulate.p.value
can be made by means of Monte Carlo simulations.
Value
A "htest"
object with elements:
statistic |
Value of the chi-squared statistic. |
df |
Degrees of freedom. |
p.value |
P-value. |
method |
A character string indicating the type of test performed. |
data.name |
A character string giving the name of the data. |
Author(s)
Jorge Castillo-Mateo
References
Benestad RE (2003). “How Often Can We Expect a Record Event?” Climate Research, 25(1), 3-13. doi:10.3354/cr025003.
Benestad RE (2004). “Record-Values, Nonstationarity Tests and Extreme Value Distributions.” Global and Planetary Change, 44(1-4), 11–26. doi:10.1016/j.gloplacha.2004.06.002.
See Also
global.test
, score.test
,
p.record
, p.regression.test
,
lr.test
Examples
# Warning, M = 76 small for the value of T = 70
p.chisq.test(ZaragozaSeries)
# Simulate p-value
p.chisq.test(ZaragozaSeries, simulate.p.value = TRUE, B = 10000)