N.record: Number of Records
In RecordTest: Inference Tools in Time Series Based on Record Statistics

N.record

R Documentation

Number of Records

Description

Returns the number of records up to time t of the values in a vector.

If the argument X is a matrix, then each column is treated as a different vector.

Usage

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

Nmean.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

The record counting process \{N_1,\ldots,N_T\} is defined by the number of records up to time t, and can be expressed in terms of the record indicator random variables I.record by

N_t = I_1 + I_2 + \ldots + I_t.

If X is a matrix with M > 1 columns, each column is treated as a vector and Nmean.record calculates for each t,

\bar N_t = \frac{N_{t1}+ \ldots + N_{tM}}{M}.

In summary:

\code{N.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} N_{1,1} & N_{1,2} & \cdots & N_{1,M} \\ N_{2,1} & N_{2,2} & \cdots & N_{2,M} \\ \vdots & \vdots & & \vdots \\ N_{T,1} & N_{T,2} & \cdots & N_{T,M} \\ \end{array} \right)

and

\code{Nmean.record}: \code{X} \longrightarrow \big( \bar{N}_1, \bar{N}_2, \cdots, \bar{N}_T \big).

Number and mean number of records for both upper and lower records can be calculated.

Value

N.record returns a numeric matrix with the number of records up to each time (row) t for a vector or each column in X. Nmean.record returns a numeric vector with the mean number of records in M series (columns) up to each time (row) t.

Note

If X is a vector both functions return the same values, N.record as a matrix and Nmean.record as a vector.

Author(s)

Jorge Castillo-Mateo

References

Arnold BC, Balakrishnan N, Nagaraja HN (1998). Records. Wiley Series in Probability and Statistics. Wiley, New York. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/9781118150412")}.

Examples

Y1 <- c( 1,  5,  3,  6,  6,  9,  2)
Y2 <- c(10,  5,  3,  6,  6,  9,  2)
Y3 <- c( 5,  7,  3,  6, 19,  2, 20)
Y  <- cbind(Y1, Y2, Y3)

N.record(Y)
Nmean.record(Y)

N.record(ZaragozaSeries)
Nmean.record(ZaragozaSeries, record = 'l')

RecordTest documentation built on Aug. 8, 2023, 1:09 a.m.