naginterfaces.library.stat.summary_​onevar_​combine

naginterfaces.library.stat.summary_onevar_combine(mrcomm)

summary_onevar_combine combines sets of summaries produced by summary_onevar().

For full information please refer to the NAG Library document for g01au

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/g01/g01auf.html

Parameters

mrcommfloat, array-like, shape $(20,b)$

The $j$th column of $mrcomm$ must contain the information returned in $\text{rcomm}$ from one of the runs of summary_onevar().

Returns

pnint

The number of valid observations, that is the number of observations with $w_i>0$, for $\text{i}=1,2,\dots ,n$.

xmeanfloat

$\overline{x}$, the mean.

xsdfloat

$s_2$, the standard deviation.

xskewfloat

$s_3$, the coefficient of skewness.

xkurtfloat

$s_4$, the coefficient of kurtosis.

xminfloat

The smallest value.

xmaxfloat

The largest value.

rcommfloat, ndarray, shape $\left(20\right)$

An amalgamation of the information held in $mrcomm$. This is in the same format as $\text{rcomm}$ from summary_onevar().

Raises

NagValueError

(errno $11$)

On entry, $b=⟨value⟩$.

Constraint: $b\ge 1$.

(errno $21$)

On entry, $mrcomm$ is not in the expected format.

Warns

NagAlgorithmicWarning

(errno $31$)

On entry, the number of valid observations is zero.

(errno $51$)

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

(errno $52$)

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

Notes

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 summary_onevar(). Then summary_onevar_combine takes the $b$ communication arrays returned by summary_onevar() and returns the mean ($\overline{x}$), 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 $\overline{x},s_2,s_3$ and $s_4$ see Notes for summary_onevar.

References

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