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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_stat_withdraw_summary_1var (g01aa)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_stat_summary_1var (g01aa) calculates the mean, standard deviation, coefficients of skewness and kurtosis, and the maximum and minimum values for a set of ungrouped data. Weighting may be used.
Note: this function is scheduled to be withdrawn, please see g01aa in Advice on Replacement Calls for Withdrawn/Superseded Routines..

Syntax

[xmean, s2, s3, s4, xmin, xmax, iwt, wtsum, ifail] = g01aa(x, 'n', n, 'wt', wt)
[xmean, s2, s3, s4, xmin, xmax, iwt, wtsum, ifail] = nag_stat_withdraw_summary_1var(x, 'n', n, 'wt', wt)
Note: the interface to this routine has changed since earlier releases of the toolbox:
At Mark 23: wt is no longer an output parameter; output parameters were reordered

Description

The data consist of a single sample of n observations, denoted by xi, with corresponding weights, wi, for i=1,2,,n.
If no specific weighting is required, then each wi is set to 1.
The quantities computed are:
(a) The sum of the weights
W=i=1nwi.  
(b) Mean
x-=i= 1nwixiW.  
(c) Standard deviation
s2=i=1nwi xi-x- 2d,   where  d=W-i=1nwi2W.  
(d) Coefficient of skewness
s3=i= 1nwi xi-x- 3 d×s23 .  
(e) Coefficient of kurtosis
s4=i=1nwi xi-x- 4 d×s24 -3.  
(f) Maximum and minimum elements of the sample.
(g) The number of observations for which wi>0, i.e., the number of valid observations. Suppose m observations are valid, then the quantities in (c), (d) and (e) will be computed if m2, and will be based on m-1 degrees of freedom. The other quantities are evaluated provided m1.

References

None.

Parameters

Compulsory Input Parameters

1:     xn – double array
The sample observations, xi, for i=1,2,,n.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the arrays x, wt. (An error is raised if these dimensions are not equal.)
n, the number of observations.
Constraint: n1.
2:     wtn – double array
If the user wishes to supply weights then the elements of wt must contain the weights associated with the observations, wi, for i=1,2,,n.

Output Parameters

1:     xmean – double scalar
The mean, x-.
2:     s2 – double scalar
The standard deviation, s2.
3:     s3 – double scalar
The coefficient of skewness, s3.
4:     s4 – double scalar
The coefficient of kurtosis, s4.
5:     xmin – double scalar
The smallest value in the sample.
6:     xmax – double scalar
The largest value in the sample.
7:     iwt int64int32nag_int scalar
iwt is used to indicate the number of valid observations, m; see (g) in Description above.
8:     wtsum – double scalar
The sum of the weights in the array wt, that is i=1nwi. This will be n if iwt was 0 on entry.
9:     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:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

   ifail=1
On entry,n<1.
W  ifail=2
The number of valid cases, m, is 1. In this case, standard deviation and coefficients of skewness and of kurtosis cannot be calculated.
   ifail=3
Either the number of valid cases is 0, or at least one weight is negative.
   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 method used is believed to be stable.

Further Comments

The time taken by nag_stat_summary_1var (g01aa) is approximately proportional to n.

Example

This example summarises an (optionally weighted) dataset and displays the results.
function g01aa_example


fprintf('g01aa example results\n\n');

% Data
x = [193     216     112     161      92     140     38      33 ...
     279     249     473     339      60     130     20      50 ...
     257     284     447      52      67      61    150    2200];
n = size(x,2);

% Get simple statistics of data
[xmean, s2, s3, s4, xmin, xmax, iwt, wtsum, ifail] = ...
g01aa(x);

fprintf('Number of cases    %7d\n',n);
fprintf('Data as input -\n');
fprintf('%12.1f%12.1f%12.1f%12.1f%12.1f\n',x)
fprintf('\n\n');
fprintf('No. of valid cases %7d\n',iwt);
fprintf('Mean               %7.1f\n',xmean);
fprintf('Minimum            %7.1f\n',xmin);
fprintf('Maximum            %7.1f\n',xmax);
fprintf('Sum of weights     %7.1f\n',wtsum);
fprintf('Std devn           %7.1f\n',s2);
fprintf('Skewness           %7.1f\n',s3);
fprintf('Kurtosis           %7.1f\n',s4);


g01aa example results

Number of cases         24
Data as input -
       193.0       216.0       112.0       161.0        92.0
       140.0        38.0        33.0       279.0       249.0
       473.0       339.0        60.0       130.0        20.0
        50.0       257.0       284.0       447.0        52.0
        67.0        61.0       150.0      2200.0

No. of valid cases      24
Mean                 254.3
Minimum               20.0
Maximum             2200.0
Sum of weights        24.0
Std devn             433.5
Skewness               3.9
Kurtosis              14.7

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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