I.record {RecordTest}

Record Indicators

Description

Returns the 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.

Usage

I.record(X, record = c("upper", "lower"), weak = FALSE)

## Default S3 method:
I.record(X, record = c("upper", "lower"), weak = FALSE)

## S3 method for class 'numeric'
I.record(X, record = c("upper", "lower"), weak = FALSE)

## S3 method for class 'matrix'
I.record(X, record = c("upper", "lower"), weak = FALSE)

Arguments

X

A numeric vector, matrix (or data frame).

record

A character string indicating the type of record to be calculated, "upper" or "lower".

weak

Logical. If TRUE, weak records are also counted. Default to FALSE.

Details

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.

In summary:

\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.

NA values in X are assigned -Inf for upper records and Inf for lower records, so they are records only if they are placed at t = 1.

Value

A binary matrix of the same length or dimension as X, indicating the record occurrence.

Author(s)

Jorge Castillo-Mateo

References

Arnold BC, Balakrishnan N, Nagaraja HN (1998). Records. Wiley Series in Probability and Statistics. Wiley, New York. doi:10.1002/9781118150412.

See Also

L.record, N.record, Nmean.record, p.record, R.record, records, S.record

Examples

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")