Geoscience Reference
In-Depth Information
uses the following formula:
h e kurtosis is a measure of whether the data are peaked or l at relative to
a normal distribution. A high kurtosis indicates that the distribution has a
distinct peak near the mean, whereas a distribution characterized by a low
kurtosis shows a l at top near the mean and broad tails. Higher peakedness
in a distribution results from rare extreme deviations, whereas a low kurtosis
is caused by frequent moderate deviations. A normal distribution has a
kurtosis of three, and some dei nitions of kurtosis therefore subtract three
from the above term in order to set the kurtosis of the normal distribution
to zero.
3.3 Examples of Empirical Distributions
As an example we can analyze the data contained in the i le
organicmatter_
one.txt
. h is i le contains the organic carbon content
C
org
of lake sediments
in weight percentage (wt%). In order to load the data, we type
clear
corg = load('organicmatter_one.txt');
h e data i le contains 60 measurements of
C
org
that can be displayed by
plot(corg,zeros(1,length(corg)),'o')
h is graph shows some of the characteristics of the data. h e organic carbon
content of the samples ranges between 9 and 15 wt%, with most of the data
clustering between 12 and 13 wt%. Values below 10 and above 14 are rare.
While this kind of representation of the data undoubtedly has its advantages,
histograms are a much more convenient way to display univariate data (Fig.
3.1). Histograms divide the range of the data into
nbin
equal intervals (also
called bins or classes), count the number of observations
n
in each bin, and
display the frequency distribution of observations as a bar plot. h e bins
are either dei ned by their edges
e
or their centers
v
. h ere is no i xed rule
for the correct number of bins; the most suitable number will depend on
the application (for example the statistical method) that is used. Ideally,
the number of bins
n
should lie between 5 and 15; it should closely rel ect
the underlying distribution and should not result in any empty bins, i.e.,
