medianHL.circular {circular}

Median using Hodges-Lehmann estimate.

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

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).

See Also

mean.circular, median.circular.

Examples

# 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")