NAG Library Function Document

nag_summary_stats_onevar (g01atc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     nb – IntegerInput

On entry: $b$, the number of observations in the current block of data. The size of the block of data supplied in x and wt can vary; therefore nb can change between calls to nag_summary_stats_onevar (g01atc).

Constraint: $\mathbf{nb}\ge 0$.

2:     x[nb] – const doubleInput

On entry: the current block of observations, corresponding to $x_{\mathit{i}}$, for $\mathit{i}=k+1,\dots ,k+b$, where $k$ is the number of observations processed so far and $b$ is the size of the current block of data.

3:     wt[nb] – const doubleInput

On entry: if wt is not NULL, wt must contain the user-supplied weights corresponding to the block of data supplied in x, that is $w_{\mathit{i}}$, for $\mathit{i}=k+1,\dots ,k+b$.

If wt is NULL, $w_i=1$ for all $i$.

Constraint: $\mathbf{wt}\left[\mathit{i}-1\right]\ge 0$, for $\mathit{i}=1,2,\dots ,\mathbf{nb}$.

4:     pn – Integer *Input/Output

On entry: the number of valid observations processed so far, that is the number of observations with $w_i>0$, for $\mathit{i}=1,2,\dots ,k$. On the first call to nag_summary_stats_onevar (g01atc), or when starting to summarise a new dataset, pn must be set to $0$.

If $\mathbf{pn}\ne 0$, it must be the same value as returned by the last call to nag_summary_stats_onevar (g01atc).

On exit: the updated number of valid observations processed, that is the number of observations with $w_i>0$, for $\mathit{i}=1,2,\dots ,k+b$.

Constraints:

• $\mathbf{pn}\ge 0$;
• if rcomm is NULL, $\mathbf{pn}=0$.

5:     xmean – double *Output

On exit: $\stackrel{-}{x}$, the mean of the first $k+b$ observations.

6:     xsd – double *Output

On exit: $s_2$, the standard deviation of the first $k+b$ observations.

7:     xskew – double *Output

On exit: $s_3$, the coefficient of skewness for the first $k+b$ observations.

8:     xkurt – double *Output

On exit: $s_4$, the coefficient of kurtosis for the first $k+b$ observations.

9:     xmin – double *Output

On exit: the smallest value in the first $k+b$ observations.

10:   xmax – double *Output

On exit: the largest value in the first $k+b$ observations.

11:   rcomm[$20$] – doubleCommunication Array

On entry: communication array, used to store information between calls to nag_summary_stats_onevar (g01atc). If $\mathbf{pn}=0$, rcomm need not be initialized, otherwise it must be unchanged since the last call to this function.

If rcomm is NULL, rcomm is not referenced and all the data must be supplied in one go.

On exit: the updated communication array. The first five elements of rcomm hold information that may be of interest with

$$\begin{array}{ccc}\hfill \mathbf{rcomm}\left[0\right]& =& \sum _{\mathit{i}=1}^{k+b}{w}_i\hfill \\ \hfill \mathbf{rcomm}\left[1\right]& =& {\left(\sum _{\mathit{i}=1}^{k+b}{w}_i\right)}^2-\sum _{\mathit{i}=1}^{k+b}{w}_i^2\hfill \\ \hfill \mathbf{rcomm}\left[2\right]& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^2\hfill \\ \hfill \mathbf{rcomm}\left[3\right]& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^3\hfill \\ \hfill \mathbf{rcomm}\left[4\right]& =& \sum _{\mathit{i}=1}^{k+b}{w}_i{\left(x_i-\stackrel{-}{x}\right)}^4\hfill & \end{array}$$

the remaining elements of rcomm are used for workspace and so are undefined.

12:   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 $⟨\mathit{\text{value}}⟩$ 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

rcomm has been corrupted between calls.

NE_INT

On entry, $\mathbf{nb}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nb}\ge 0$.

On entry, $\mathbf{pn}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{rcomm}\text{is}\mathbf{NULL}$ then $\mathbf{pn}=0$.

On entry, $\mathbf{pn}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{pn}\ge 0$.

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_NEG_WEIGHT

On entry, $\mathbf{wt}\left[⟨\mathit{\text{value}}⟩\right]=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{wt}\text{is not}\mathbf{NULL}$ then $\mathbf{wt}\left[\mathit{i}-1\right]\ge 0$, for $\mathit{i}=1,2,\dots ,\mathbf{nb}$.

NE_PREV_CALL

On entry, $\mathbf{pn}=⟨\mathit{\text{value}}⟩$.
On exit from previous call, $\mathbf{pn}=⟨\mathit{\text{value}}⟩$.
Constraint: if $\mathbf{pn}>0$, pn must be unchanged since previous call.

NE_ZERO_VARIANCE

On exit we were unable to calculate xskew or xkurt. A value of $0$ has been returned.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01atce.c)

10.2  Program Data

Program Data (g01atce.d)

10.3  Program Results

Program Results (g01atce.r)