Davison & Smith (1990) empirical mean excess over a threshold grid

Usage

MeanExc(x, u_grid = NULL, conf_level = 0.95)

Arguments

x: numeric sample
u_grid: thresholds; default the sorted distinct values of x with the largest dropped
conf_level: level for the pointwise normal limits

Value

list(u, e, se, sd_excess, ci_lower, ci_upper, n_exceed, n)

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
MeanExc(V)
#> $u
#> [1] 1 2 3 4 5 6 7
#> 
#> $e
#> [1] 4.0 3.5 3.0 2.5 2.0 1.5 1.0
#> 
#> $se
#> [1] 0.8164966 0.7637626 0.7071068 0.6454972 0.5773503 0.5000000       NaN
#> 
#> $sd_excess
#> [1] 2.1602469 1.8708287 1.5811388 1.2909944 1.0000000 0.7071068       NaN
#> 
#> $ci_lower
#> [1] 2.3996961 2.0030528 1.6140962 1.2348487 0.8684143 0.5200180       NaN
#> 
#> $ci_upper
#> [1] 5.600304 4.996947 4.385904 3.765151 3.131586 2.479982      NaN
#> 
#> $n_exceed
#> [1] 7 6 5 4 3 2 1
#> 
#> $conf_level
#> [1] 0.95
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Davison & Smith (1990) mean excess e(u)=E[X-u|X>u]; linear in u above a generalised Pareto threshold"
#>