naginterfaces.library.univar.robust_​1var_​median

naginterfaces.library.univar.robust_1var_median(x)[source]

robust_1var_median finds the median, median absolute deviation, and a robust estimate of the standard deviation for a set of ungrouped data.

For full information please refer to the NAG Library document for g07da

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/g07/g07daf.html

Parameters
xfloat, array-like, shape

The vector of observations, .

Returns
yfloat, ndarray, shape

The observations sorted into ascending order.

xmefloat

The median, .

xmdfloat

The median absolute deviation, .

xsdfloat

The robust estimate of the standard deviation, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

The data consists of a sample of size , denoted by , drawn from a random variable .

robust_1var_median first computes the median,

and from this the median absolute deviation can be computed,

Finally, a robust estimate of the standard deviation is computed,

where is the value of the inverse standard Normal function at the point .

robust_1var_median is based upon function LTMDDV within the ROBETH library, see Marazzi (1987).

References

Huber, P J, 1981, Robust Statistics, Wiley

Marazzi, A, 1987, Subroutines for robust estimation of location and scale in ROBETH, Cah. Rech. Doc. IUMSP, No. 3 ROB 1, Institut Universitaire de Médecine Sociale et Préventive, Lausanne