# Computing trimmed measures of sherical location

### Description

Computes a sample trimmed measure of location based on the spherical Tukey's depth. Supports data on the circle or on the sphere (for Circular median only).

### Usage

1 | ```
strmeasure(P,sorted=FALSE,depths=NULL,alpha=0,method="Mean")
``` |

### Arguments

`P` |
The data as a vector, a matrix, a data frame or a list. |

`sorted` |
Logical; if TRUE, it indicates that the data given in first argument is sorted. |

`depths` |
An optionnal vector of the same length of P that contains the Tukey's depth of each data. The calculation of the depth is then skipped and the provided values are used instead. |

`alpha` |
An optionnal numeric value between 0 and 1 to compute the median on a trimmed region rather than on the whole dataset. The trimming keeps only those points with a depth greater than or equal to |

`method` |
Character string which determines the measure used. |

### Details

This function returns a location estimate (Tukey's median or mean direction) of a sample truncated by Tukey's depth. For data on the circle, data must be expressed in polar coordinates as a angle in radians with values between 0 and *2π*. Data on the sphere can be expressed in Euclidean coordinates (*n* by 3 matrix) or in spherical coordinates (*n* by 2 matrix) where the first column contains *θ* and the second column *φ*. The type of coordinates is determined automatically based on the dimensions of the input.

While the option `method="Tukey"`

supports only data on the circle, `method="Mean"`

can also handle data on the sphere.

### Value

If the input sample is on the circle, a numeric value between *0* and *2π* giving the trimmed measure. If the input sample is on the sphere, the trimmed measure in Euclidean coordinates.

### Author(s)

Maxime Genest.

### References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), *Ann. Statist.*, **27**, 783–858.

Mardia, K.V. and Jupp, E.J. (1999). *Directional Statistics*, Wiley.

### See Also

`sdepth`

for the calculation of the depth of a point, `scontour`

for Tukey's spherical median.

### Examples

1 2 3 4 5 6 7 |