# medianHL.circular: Median using Hodges-Lehmann estimate. In circular: Circular Statistics

## Description

Sample median for a vector of data using Hodges-Lehmann estimate and Sample median direction measure for a vector of circular data using Hodges-Lehmann estimate.

## Usage

 ```1 2 3 4 5 6 7``` ```medianHL(x, na.rm=FALSE, ...) ## Default S3 method: medianHL(x, na.rm=FALSE, method=c("HL1","HL2","HL3"), prop=NULL) ## S3 method for class 'circular' medianHL(x, na.rm=FALSE, method=c("HL1","HL2","HL3"), prop=NULL) ```

## Arguments

 `x` a vector. For the function `medianHL.circular` the object is coerced to class `circular`. `na.rm` logical, indicating if `NA`'s should be omitted. `method` The method used to calculate the median, see details below. `prop` The proportion of pairs that are sampled. If `NULL` all combinations are used. It must be a number in the interval (0,1) or `NULL`. `...` further arguments passed to the next method.

## Details

The algorithm is as follows:

The algorithm will create pairs of elements of the vector `x`.

It will calculate the circular mean on those pairs.

It will calculate the circular median on these averages.

The type of pairs considered are controlled by `method`:

if `method` is "HL1" are considered unordered pairs without replications and repetition in the number of `(n*(n-1))/2` pairs;

if `method` is "HL2" are considered unordered pairs without replications in the number of `(n*(n+1))/2` pairs;

if `method` is "HL3" all pairs are considered in the number of `n^2`.

If `prop` is not `NULL`, the algorithm will consider a subsample following the rules specified by `method`, however, the number of pairs considered is prop * (number of pairs defined by `method`).

For more details see Bennett Sango Otieno, 'An Alternative Estimate of Preferred Direction for Circular Data', Virginia Tech (2002) pag. 27-28 and 46-47.

## Value

For `medianHL.circular` the median is returned as an object of class `circular` with the attribute given by those of `x`. An attributes `medians` reports all the averages which are minimizer of the circular median function.

## Author(s)

Claudio Agostinelli and Alessandro Gagliardi.

## References

Bennett Sango Otieno, An Alternative Estimate of Preferred Direction for Circular Data, Virginia Tech (July 2002).

Bennett Sango Otieno and Christine M. Anderson-Cook,Measures of preferred direction for environmental and ecological circular data, Springer (June 2004).

`mean.circular`, `median.circular`.
 ```1 2 3 4 5 6``` ```# Compute the median direction of a random sample of observations. x <- circular(runif(50, circular(0), pi)) # Calculate the three medians for each method without \code{prop} argument. medianHL.circular(x,method="HL1") medianHL.circular(x,method="HL2") medianHL.circular(x,method="HL3") ```