NAG Library Routine Document

G07DAF

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

5 Parameters

1: $N$ – INTEGERInput: On entry: $n$ , the number of observations.

Constraint: $N > 1$ .
2: $X (N)$ – REAL (KIND=nag_wp) arrayInput: On entry: the vector of observations, $x_{1}, x_{2}, \dots, x_{n}$ .
3: $Y (N)$ – REAL (KIND=nag_wp) arrayOutput: On exit: the observations sorted into ascending order.
4: $XME$ – REAL (KIND=nag_wp)Output: On exit: the median, $θ_{med}$ .
5: $XMD$ – REAL (KIND=nag_wp)Output: On exit: the median absolute deviation, $σ_{med}$ .
6: $XSD$ – REAL (KIND=nag_wp)Output: On exit: the robust estimate of the standard deviation, $σ_{med}^{'}$ .
7: $IFAIL$ – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,

N \leq 1

$IFAIL = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.8 in the Essential Introduction for further information.

$IFAIL = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.7 in the Essential Introduction for further information.

$IFAIL = - 999$: Dynamic memory allocation failed.
See Section 3.6 in the Essential Introduction for further information.

7 Accuracy

The computations are believed to be stable.

8 Parallelism and Performance

G07DAF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

G07DAF makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

Unless otherwise stated in the Users' Note, the routine may be called with the same actual array supplied for parameters X and Y, in which case the sorted data values will overwrite the original contents of X. However this is not standard Fortran, and may not work on all systems.

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 Routine DocumentG07DAF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References