NAG Library Function Document

nag_summary_stats_onevar_combine (g01auc)

void	nag_summary_stats_onevar_combine (Integer b, const double mrcomm[], Integer pn, double xmean, double xsd, double xskew, double xkurt, double xmin, double xmax, double rcomm[], NagError fail)

3 Description

Assume a dataset containing

n

observations, denoted by

x = \{x_{i} : i = 1, 2, \dots, n\}

and a set of weights,

w = \{w_{i} : i = 1, 2, \dots, n\}

, has been split into

b

blocks, and each block summarised via a call to nag_summary_stats_onevar (g01atc). Then nag_summary_stats_onevar_combine (g01auc) takes the

b

communication arrays returned by nag_summary_stats_onevar (g01atc) and returns the mean (

\bar{x}

), standard deviation (

s_{2}

), coefficients of skewness (

s_{3}

) and kurtosis (

s_{4}

), and the maximum and minimum values for the whole dataset.

For a definition of

\bar{x}, s_{2}, s_{3}

and

s_{4}

see Section 3 in nag_summary_stats_onevar (g01atc).

4 References

West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555

5 Arguments

1: b – IntegerInput: On entry: $b$ , the number of blocks the full dataset was split into.
Constraint: $b \geq 1$ .
2: mrcomm[ $20 \times b$ ] – const doubleCommunication Array: Note: where $MRCOMM (i, j)$ appears in this document, it refers to the array element $mrcomm [(j - 1) \times 20 + i - 1]$ .
On entry: the $j$ th column of MRCOMM must contain the information returned in rcomm from one of the runs of nag_summary_stats_onevar (g01atc).
3: pn – Integer *Output: On exit: the number of valid observations, that is the number of observations with $w_{i} > 0$ , for $i = 1, 2, \dots, n$ .
4: xmean – double *Output: On exit: $\bar{x}$ , the mean.
5: xsd – double *Output: On exit: $s_{2}$ , the standard deviation.
6: xskew – double *Output: On exit: $s_{3}$ , the coefficient of skewness.
7: xkurt – double *Output: On exit: $s_{4}$ , the coefficient of kurtosis.
8: xmin – double *Output: On exit: the smallest value.
9: xmax – double *Output: On exit: the largest value.
10: rcomm[ $20$ ] – doubleCommunication Array: On exit: an amalgamation of the information held in mrcomm. This is in the same format as rcomm from nag_summary_stats_onevar (g01atc).
If rcomm is NULL, rcomm is not referenced.
11: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_CASES_ONE: On exit we were unable to calculate xsd, xskew or xkurt. A value of $0$ has been returned.
NE_CASES_ZERO: On entry, the number of valid observations is zero.
NE_ILLEGAL_COMM: On entry, mrcomm is not in the expected format.
NE_INT: On entry, $b = ⟨value⟩$ .
Constraint: $b \geq 1$ .
NE_INTERNAL_ERROR: 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.
NE_ZERO_VARIANCE: On exit we were unable to calculate xskew or xkurt. A value of $0$ has been returned.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

The order that the

b

communication arrays are stored in mrcomm is arbitrary. Different orders can lead to slightly different results due to numerical accuracy of floating-point calculations.

Both nag_summary_stats_onevar_combine (g01auc) and nag_summary_stats_onevar (g01atc) consolidate results from multiple summaries. Whereas the former can only be used to combine summaries calculated sequentially, the latter combines summaries calculated in an arbitrary order allowing, for example, summaries calculated on different processing units to be combined.

10 Example

This example summarises some simulated data. The data is supplied in three blocks, the first consisting of

21

observations, the second

51

observations and the last

28

observations. Summaries are produced for each block of data separately and then an overall summary is produced.

NAG Library Function Documentnag_summary_stats_onevar_combine (g01auc)

+− Contents

1 Purpose

2 Specification