Mean residual life plot

Formula: e(u) = mean(X - u | X > u)

Usage

Evmrlp(x, u_grid = NULL)

Arguments

x

Sample.

u_grid

Thresholds, or NULL for twenty equally spaced values from the minimum to the 90th percentile.

Value

List with u, e_u, se, n_exceed, estimate (slope), n, method.

Details

Linear in u above a threshold where the GPD holds, with slope xi/(1-xi) and intercept sigma_u0/(1-xi); constant when xi = 0. That linearity is what the plot is read for.

References

Davison & Smith (1990), JRSS B 52(3):393-442.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Evmrlp(V)
#> $u
#>  [1] 1.000000 1.331579 1.663158 1.994737 2.326316 2.657895 2.989474 3.321053
#>  [9] 3.652632 3.984211 4.315789 4.647368 4.978947 5.310526 5.642105 5.973684
#> [17] 6.305263 6.636842 6.968421
#> 
#> $e_u
#>  [1] 4.0000000 3.6684211 3.3368421 3.0052632 3.1736842 2.8421053 2.5105263
#>  [8] 2.6789474 2.3473684 2.0157895 2.1842105 1.8526316 1.5210526 1.6894737
#> [15] 1.3578947 1.0263158 1.1947368 0.8631579 0.5315789
#> 
#> $se
#>  [1] 0.8164966 0.8164966 0.8164966 0.8164966 0.7637626 0.7637626 0.7637626
#>  [8] 0.7071068 0.7071068 0.7071068 0.6454972 0.6454972 0.6454972 0.5773503
#> [15] 0.5773503 0.5773503 0.5000000 0.5000000 0.5000000
#> 
#> $n_exceed
#>  [1] 7 7 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2
#> 
#> $estimate
#> [1] -0.5238095
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "mean residual life (mean excess) plot"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"