1: $x (n)$ – double array: The sample observations, $x_{i}$ , for $i = 1, 2, \dots, n$ .
2: $alpha$ – double scalar: $α$ , the proportion of observations to be trimmed at each end of the sorted sample.

Constraint: $0.0 \leq alpha < 0.5$ .

Optional Input Parameters

1: $n$ – int64int32nag_int scalar: Default: the dimension of the array x.
$n$ , the number of observations.

Constraint: $n \geq 2$ .

Output Parameters

1: $tmean$ – double scalar: The $α$ -trimmed mean, ${\bar{x}}_{t}$ .
2: $wmean$ – double scalar: The $α$ -Winsorized mean, ${\bar{x}}_{w}$ .
3: $tvar$ – double scalar: Contains an estimate of the variance of the trimmed mean.
4: $wvar$ – double scalar: Contains an estimate of the variance of the Winsorized mean.
5: $k$ – int64int32nag_int scalar: Contains the number of observations trimmed at each end, $k$ .
6: $sx (n)$ – double array: Contains the sample observations sorted into ascending order.
7: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,

n \leq 1

$ifail = 2$

On entry,	$alpha < 0.0$ ,
or	$alpha \geq 0.5$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

The results should be accurate to within a small multiple of machine precision.

Further Comments

The time taken is proportional to

n

Example

The following program finds the

α

-trimmed mean and

α

-Winsorized mean for a sample of

16

observations where

α = 0.15

. The estimates of the variances of the above two means are also calculated.

Open in the MATLAB editor: g07dd_example

function g07dd_example


fprintf('g07dd example results\n\n');

x = [26; 12;  9;  2;  5;  6;  8; 14;
      7;  3;  1; 11; 10;  4; 17; 21];
alpha = 0.15;

[tmean, wmean, tvar, wvar, k, sx, ifail] = ...
  g07dd(x, alpha);

% Calculate proportion of data cut
propn = 100*(1-2*double(k)/numel(x));

fprintf('Statistics from middle %6.2f%% of data\n\n',propn);
fprintf('               Trimmed-mean = %11.4f\n', tmean);
fprintf('   Variance of Trimmed-mean = %11.4f\n\n', tvar);
fprintf('            Winsorized-mean = %11.4f\n', wmean);
fprintf('Variance of Winsorized-mean = %11.4f\n', wvar);

g07dd example results

Statistics from middle  75.00% of data

               Trimmed-mean =      8.8333
   Variance of Trimmed-mean =      1.5434

            Winsorized-mean =      9.1250
Variance of Winsorized-mean =      1.5381

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox