Upper record times and counts in a sequence

Formula: R_n = sum_i 1{X_i > max(X_1..X_{i-1})}; E[R_n] = sum_i 1/i; Var[R_n] = sum_i (1/i - 1/i^2)

Usage

Evtrecords(x)

Arguments

x

See Usage.

Value

List with count, times (indices of records), values, expected, variance, z, n.

References

Arnold, Balakrishnan and Nagaraja (1998), Records, Wiley. Not held locally; the indicator representation and the resulting harmonic mean and variance are standard published results for iid continuous data.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Evtrecords(V)
#> $count
#> [1] 8
#> 
#> $times
#> [1] 0 1 2 3 4 5 6 7
#> 
#> $values
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $expected
#> [1] 2.717857
#> 
#> $variance
#> [1] 1.190435
#> 
#> $z
#> [1] 4.841247
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Upper record times and counts"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"