nag_summary_stats_1var (g01aac) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_summary_stats_1var (g01aac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_summary_stats_1var (g01aac) 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.

2  Specification

#include <nag.h>
#include <nagg01.h>
void  nag_summary_stats_1var (Integer n, const double x[], const double wt[], Integer *nvalid, double *xmean, double *xsd, double *xskew, double *xkurt, double *xmin, double *xmax, double *wsum, NagError *fail)

3  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
(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.

4  References


5  Arguments

1:     nIntegerInput
On entry: n, the number of observations.
Constraint: n1.
2:     x[n]const doubleInput
On entry: the sample observations, xi, for i=1,2,,n.
3:     wt[n]const doubleInput
On entry: if weights are being supplied then the elements of wt must contain the weights associated with the observations, wi, for i=1,2,,n.
If weights are not supplied then wt must be set to the null pointer, i.e., (double *)0.
4:     nvalidInteger *Output
On exit: is used to indicate the number of valid observations, m; see Section 3 (g).
5:     xmeandouble *Output
On exit: the mean, x-.
6:     xsddouble *Output
On exit: the standard deviation, s2.
7:     xskewdouble *Output
On exit: the coefficient of skewness, s3.
8:     xkurtdouble *Output
On exit: the coefficient of kurtosis, s4.
9:     xmindouble *Output
On exit: the smallest value in the sample.
10:   xmaxdouble *Output
On exit: the largest value in the sample.
11:   wsumdouble *Output
On exit: the sum of the weights in the array wt, that is i=1nwi. This will be n if weighted estimates are not used.
12:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
The number of valid cases is one. The standard deviation and coefficients of skewness and of kurtosis cannot be calculated.
The number of valid cases is zero.
On entry, n=value.
Constraint: n1.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
On entry, wt[value] = value.
Constraint: wt[value] 0.0 .

7  Accuracy

The method used is believed to be stable.

8  Further Comments

The time taken by nag_summary_stats_1var (g01aac) is approximately proportional to n.

9  Example

This example summarises a number of datasets. For each dataset the observations and, optionally, weights are read and printed. nag_summary_stats_1var (g01aac) is then called and the calculated quantities are printed.

9.1  Program Text

Program Text (g01aace.c)

9.2  Program Data

Program Data (g01aace.d)

9.3  Program Results

Program Results (g01aace.r)

nag_summary_stats_1var (g01aac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012