Trimmed L-moments TL(s,t) of a sample

Formula: lambda_r^(s,t) = (1/r) sum_k (-1)^k C(r-1,k) E[X_(r+s-k):(r+s+t)]

Usage

Evtlmom(x, s = 0, t = 0, order = 2)

Arguments

x

Sample.

s

Left trimming.

t

Right trimming.

order

Highest order r to compute.

Value

List with lambda, estimate, tau, n, method.

Details

with the order statistic expectation estimated by the unbiased combinatorial weights E[X_(j:m)] = sum_i C(i-1,j-1) C(n-i,m-j) / C(n,m) x_(i). Trimming s observations from the left and t from the right makes the moments exist for heavy tails where ordinary L-moments do not. With s = t = 0 they reduce to Hosking's L-moments, so lambda_1 is the sample mean and lambda_2 the L-scale.

References

Elamir & Seheult (2003), Comput. Statist. Data Anal. 43(3):299-314.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Evtlmom(V)
#> $lambda
#> [1] 4.5 1.5
#> 
#> $estimate
#> [1] 1.5
#> 
#> $tau
#> [1] NaN NaN
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "trimmed L-moments TL(s,t)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"