Returns the sample record indicators of the values in a vector. The record indicator for each value in a vector is a binary variable which takes the value 1 if the corresponding value in the vector is a record and 0 otherwise.
If the argument X is a matrix, then each column is treated as a
different vector.
I.record(X, record = c("upper", "lower"), weak = FALSE)# S3 method for default
I.record(X, record = c("upper", "lower"), weak = FALSE)
# S3 method for numeric
I.record(X, record = c("upper", "lower"), weak = FALSE)
# S3 method for matrix
I.record(X, record = c("upper", "lower"), weak = FALSE)
A numeric vector, matrix (or data frame).
A character string indicating the type of record to be calculated, "upper" or "lower".
Logical. If TRUE, weak records are also counted. Default
to FALSE.
A binary matrix of the same length or dimension as X,
indicating the record occurrence.
Let \(\{X_1,\ldots,X_T\}\) be a vector of random variables of size \(T\). An observation \(X_t\) will be called an upper record value if its value exceeds that of all previous observations. An analogous definition deals with lower record values. Here, \(X_1\) is referred to as the reference value or the trivial record. Then, the sequence of record indicator random variables \(\{I_1,\ldots,I_T\}\) is given by $$I_t = \left\{ \begin{array}{ll} 1 & \mbox{if } X_t \mbox{ is a record,} \\ 0 & \mbox{if } X_t \mbox{ is not a record.} \end{array} \right.$$
The method I.record calculates the sample sequence above if the
argument X is a numeric vector. If the argument X is a
matrix (or data frame) with \(M\) columns, the method I.record
calculates the sample sequence above for each column of the object as if
all columns were different sequences.
Summarily: $$\code{I.record}: \code{X} = \left( \begin{array}{cccc} X_{1,1} & X_{1,2} & \cdots & X_{1,M} \\ X_{2,1} & X_{2,2} & \cdots & X_{2,M} \\ \vdots & \vdots & & \vdots \\ X_{T,1} & X_{T,2} & \cdots & X_{T,M} \\ \end{array} \right) \longrightarrow \left( \begin{array}{cccc} I_{1,1} & I_{1,2} & \cdots & I_{1,M} \\ I_{2,1} & I_{2,2} & \cdots & I_{2,M} \\ \vdots & \vdots & & \vdots \\ I_{T,1} & I_{T,2} & \cdots & I_{T,M} \\ \end{array} \right).$$
Indicators of record occurrence can be calculated for both upper and lower records.
All the procedure above can be extended to weak records, which also count
the ties as a new (weak) record. Ties are possible in discrete variables
or if a continuous variable has been rounded. Weak records can be computed
if weak = TRUE.
Arnold BC, Balakrishnan N, Nagaraja HN (1998). Records. Wiley Series in Probability and Statistics. Wiley, New York.
L.record,
N.record, Nmean.record,
p.record, R.record,
records, S.record
# NOT RUN {
X <- c(1, 5, 3, 6, 6, 9, 2, 11, 17, 8)
I.record(X)
I.record(X, weak = TRUE)
I.record(ZaragozaSeries)
# record argument can be shortened
I.record(ZaragozaSeries, record = "l")
# }
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