p.record {RecordTest}

Probabilities of Record

Description

S.record and p.record return the sample number of records and mean number of records at each time t in a set of M vectors (columns of X), respectively. In particular, p.record is the estimated record probability at each time t.

(For the introduccion to records see Details in I.record.)

Usage

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

S.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

Given a matrix formed by M vectors (columns), measured at T times (rows), M.record calculates the number of records in the M vectors at each observed time t, S_t.

The function p.record is equivalent, but calculates the proportion of records at each time t, that is the ratio:

\hat p_t = \frac{S_t}{M} = \frac{I_{t,1} + \ldots + I_{t,M}}{M},

this proportion is an estimation of the probability of record at that time.

Following the notation in I.record, in summary:

\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) \begin{array}{lc} \stackrel{\code{S.record}}{\longrightarrow} & \Big( S_1, S_2, \cdots, S_T \Big) \\ \\ \stackrel{\code{p.record}}{\longrightarrow} & \Big( \hat p_1, \hat p_2, \cdots, \hat p_T \Big) \\ \end{array}

Summaries for both upper and lower records can be calculated.

Value

A vector with the number (or proportion in the case of p.record) of records at each time t (row).

Author(s)

Jorge Castillo-Mateo

References

Cebrián AC, Castillo-Mateo J, Asín J (2022). “Record Tests to Detect Non Stationarity in the Tails with an Application to Climate Change.” Stochastic Environmental Research and Risk Assessment, 36(2), 313-330. doi:10.1007/s00477-021-02122-w.

See Also

I.record, L.record, N.record, Nmean.record, R.record, records

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)

S.record(Y)
p.record(Y)

S.record(ZaragozaSeries)
p.record(ZaragozaSeries, record = "l")