Survey median

The weighted CDF inverted at one half, delegated to Svyqtl so the estimator and its Woodruff interval are shared rather than reimplemented. The weighted mean is reported alongside so the skewness of the weighted distribution is visible.

Usage

Svymed(y, weights = NULL)

Arguments

y

Numeric observations.

weights

Optional design weights; equal weights if NULL.

Value

List with estimate, se, lower, upper, F, mean, sumw, n, method.

Details

Formula: M = inf{t : F_w(t) >= 1/2}.

References

Francisco, C. A. and Fuller, W. A. (1991). Quantile estimation with a complex survey design. The Annals of Statistics 19(1):454-469. doi:10.1214/aos/1176347993

Examples

Svymed(c(1, 2, 3, 4, 5))
#> $estimate
#> [1] 3
#> 
#> $se
#> [1] 0.219089
#> 
#> $lower
#> [1] 1
#> 
#> $upper
#> [1] 5
#> 
#> $F
#> [1] 0.6
#> 
#> $mean
#> [1] 3
#> 
#> $sumw
#> [1] 5
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "weighted median, F_w inverted at 1/2 [Francisco & Fuller 1991]"
#>