NAG Library Routine Document

G01AAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

On entry: $n$, the number of observations.

Constraint: $\mathbf{N}\ge 1$.

2:     X(N) – REAL (KIND=nag_wp) arrayInput

On entry: the sample observations, $x_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

3:     IWT – INTEGERInput/Output

On entry: indicates whether weights are to be supplied by you or not. In the latter case, the weights will be assumed equal and assigned the value $1.0$ in the routine.

$\mathbf{IWT}=0$

Indicates no user-supplied weights.

$\mathbf{IWT}=1$

Indicates user-supplied weights are required, and they will be supplied in the array WT.

On exit: IWT is used to indicate the number of valid observations, $m$; see (g) in Section 3 above.

4:     WT(N) – REAL (KIND=nag_wp) arrayInput/Output

On entry: if $\mathbf{IWT}=1$, the elements of WT must contain the weights associated with the observations, $w_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

If $\mathbf{IWT}=0$, the elements of WT need not be set.

On exit: if $\mathbf{IWT}=1$, the elements of WT are unchanged.

If $\mathbf{IWT}=0$, each element of WT will be assigned the value $1.0$.

5:     XMEAN – REAL (KIND=nag_wp)Output

On exit: the mean, $\stackrel{-}{x}$.

6:     S2 – REAL (KIND=nag_wp)Output

On exit: the standard deviation, $s_2$.

7:     S3 – REAL (KIND=nag_wp)Output

On exit: the coefficient of skewness, $s_3$.

8:     S4 – REAL (KIND=nag_wp)Output

On exit: the coefficient of kurtosis, $s_4$.

9:     XMIN – REAL (KIND=nag_wp)Output

On exit: the smallest value in the sample.

10:   XMAX – REAL (KIND=nag_wp)Output

On exit: the largest value in the sample.

11:   WTSUM – REAL (KIND=nag_wp)Output

On exit: the sum of the weights in the array WT, that is ${\displaystyle \sum _{i=1}^n}{w}_i$. This will be N if IWT was $0$ on entry.

12:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. 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 $-1\text{ or }1$ 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 $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

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

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,

$\mathbf{N}<1$.

$\mathbf{IFAIL}=2$

The number of valid cases, $m$, is $1$. In this case, standard deviation and coefficients of skewness and of kurtosis cannot be calculated.

$\mathbf{IFAIL}=3$

Either the number of valid cases is $0$, or at least one weight is negative.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01aafe.f90)

9.2  Program Data

Program Data (g01aafe.d)

9.3  Program Results

Program Results (g01aafe.r)