# HL: Hodges-Lehmann estimate In rQCC: Robust Quality Control Chart

## Description

Calculates the Hodges-Lehmann estimate.

## Usage

 `1` ```HL(x, method = c("HL1", "HL2", "HL3"), na.rm = FALSE) ```

## Arguments

 `x` a numeric vector of observations. `method` a character string specifying the estimator, must be one of `"HL1"` (default), `"HL2"` and `"HL3"`. `na.rm` a logical value indicating whether NA values should be stripped before the computation proceeds.

## Details

`HL` computes the Hodges-Lehmann estimates (one of `"HL1"`, `"HL2"`, `"HL3"`).

The Hodges-Lehmann (HL1) is defined as

HL1 = median of (Xi+Xj)/2 over i<j

where i, j=1,2,...,n.

The Hodges-Lehmann (HL2) is defined as

HL2 = median of (Xi+Xj)/2 over i ≤ j.

The Hodges-Lehmann (HL3) is defined as

HL3 = median of (Xi+Xj)/2 over all (i,j).

## Value

It returns a numeric value.

## Author(s)

Chanseok Park and Min Wang

## References

Park, C., H. Kim, and M. Wang (2020). Investigation of finite-sample properties of robust location and scale estimators. Communications in Statistics - Simulation and Computation, To appear.
https://doi.org/10.1080/03610918.2019.1699114

Hodges, J. L. and E. L. Lehmann (1963). Estimates of location based on rank tests. Annals of Mathematical Statistics, 34, 598–611.

`finite.breakdown`{rQCC} for calculating the finite-sample breakdown point.
 ```1 2``` ```x = c(0:10, 50) HL(x, method="HL2") ```