NAG Library Function Document

nag_median_1var (g07dac)

is the value of the inverse standard Normal function at the point 0.75. nag_median_1var (g07dac) is based upon the algorithm used in the function LTMDDV in the ROBETH library, see Marazzi (1987).

4 References

Huber P J (1981) Robust Statistics Wiley

Marazzi A (1987) Subroutines for robust and bounded influence regression in ROBETH Cah. Rech. Doc. IUMSP, No. 3 ROB 2 Institut Universitaire de Médecine Sociale et Préventive, Lausanne

5 Arguments

1: n – IntegerInput: On entry: the number of observations, $n$ .
Constraint: $n > 1$ .
2: x[n] – const doubleInput: On entry: the vector of observations, $x_{1}, x_{2}, \dots, x_{n}$ .
3: y[n] – doubleOutput: On exit: the observations sorted into ascending order.
4: xme – double *Output: On exit: the median, $θ_{med}$ .
5: xmd – double *Output: On exit: the median absolute deviation, $σ_{med}$ .
6: xsd – double *Output: On exit: the robust estimate of the standard deviation, $σ_{med}^{'}$ .
7: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_INT_ARG_GT: On entry, $n = ⟨value⟩$ .
Constraint: $n \leq ⟨value⟩$ .
NE_INT_ARG_LE: On entry, $n = ⟨value⟩$ .
Constraint: $n > 1$ .

7 Accuracy

The computations are believed to be stable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

nag_median_1var (g07dac) may be called with the same actual array supplied for arguments x and y, in which case the sorted data values will overwrite the original contents of x.

10 Example

The following program reads in a set of data consisting of eleven observations of a variable x. The median, median absolute deviation and a robust estimate of the standard deviation are calculated and printed along with the sorted data in output array y.

NAG Library Function Documentnag_median_1var (g07dac)

+− Contents

1 Purpose

2 Specification

3 Description