Poleward of 
, the mean values and the standard deviations
of the electron density and core temperature deduced from the Gaussian fittings
are close to those of the measured
histograms given respectively in Table 2 and Table 3.
This suggests that the fitted curves are rather well suited
to describe the data in the
high-speed streams, especially for the electron density where the 
of the Gaussian fitting is only about 6%.
| Latitude Intervals | ||
| Moments |  S | N |
| Number of points | 52,800 | 45,500 |
| Mean |  |  |
| Standard deviation |  |  |
| Skewness | 0.4 | 0.8 |
| Kurtosis | 0.6 | 2 |
| Latitude Intervals | ||
| Moments | S | N |
| Number of points | 52,800 | 45,500 |
| Mean |  K |  K |
| Standard deviation |  K |  K |
| Skewness | 4.8 | 2.7 |
| Kurtosis | 72 | 32 |
To settle this point more precisely, we calculated the first four cumulants of the distributions, i.e., the mean, variance, skewness, and kurtosis (see, e.g., [Kendall & Stuart, 1969]).
The skewness and kurtosis are nondimensional moments,
contrary to the mean and standard deviation which have the same dimension as
the measured quantities.
The skewness
characterizes the degree of asymmetry of the distribution around its
mean. A positive (negative) value of the skewness implies a distribution
with a
higher number of large (small) values of the parameter than would be
expected for a Gaussian. The kurtosis measures the relative
peakness or flatness of a distribution compared to a normal distribution, with
the same mean and standard deviation;
the larger the kurtosis, the more peaked
the distribution.
For a Gaussian distribution,
the skewness and kurtosis are zero, with variances respectively equal to
and
,
where N is the number of points.
We can believe in the skewness and kurtosis values
only when they are several times
as large as these values. It is always the case in our results (Tables 2
and 3), where
the variance of the skewness and
kurtosis are about 0.01 and 0.02, respectively.
Only
if the distributions are normal, do the mean and the standard deviation
completely characterize them, and they have
no higher cumulants such as the skewness or the kurtosis.
Tables 2 and 3 give the four moments of the electron density and temperature
distributions defined above for
different latitudinal regions.
The skewness and kurtosis of the electron density
are small poleward of , especially southward of S,
but the distribution differs from a Gaussian
since the third and fourth moments are significantly
different from zero.
Likewise,
one can see that the distribution of the core temperature
is non Gaussian
because the skewness and the kurtosis have significant values.
The high value
of the skewness and the positive value of the kurtosis, shown in Table 3,
reflect the large number of high temperature values.
The density data set is more Gaussian
distributed than the temperature data set.
Note that the mean values of the electron density obtained poleward of
are close to those deduced by
[Schwenn, 1983], about 
, from
Helios measurements for high-speed flow near solar activity minimum.
In similar conditions,
[Pilipp et al., 1990] obtained a core
electron density in the range K to 
K.
Our result of K is thus close to the lower limit of the
reported high-speed stream value near solar minimum.
Our histograms confirm the existence
of
a single class of steady flow with a low mean
density and temperature
in the
fast wind coming
from polar coronal holes.