| N.record {RecordTest} | 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 |
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. doi:10.1002/9781118150412.
See Also
I.record, L.record,
p.record, R.record,
records, S.record
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')