Graphics Reference
In-Depth Information
A density histogram, in contrast, plots
ν
j
nh
j
f
(
x
)=
x
B
j
.
(
.
)
A simple calculation demonstrates that the density histogram integrates to
and is
therefore a true density, and it can be shown to provide a reasonable estimate of f .
he use of h
j
in rescaling means that f will be well estimated, even with varying bin
widths.
See Fig.
.
foran example ofa density histogram. hedata consist of average win-
ter (December, January, and February) temperature minimums, in degrees Celsius,
for n
,
grid points in the US state of Colorado over the period
-
.
his
-yearaverageoftemperatureminimums, aswellasaveragetemperaturemaxi-
mums (degrees Celsius) andtotal precipitation (millimeters),wereconstructed from
monthly datasets available from the Spatial Climate Analysis Service at Oregon State
University (http://www.ocs.oregonstate.edu/prism/). hesehigh-resolution, gridded
datasets are based on the parameter-elevation regressions on the independent slopes
model (PRISM) discussed in Daly et al. (
) and Gibson et al. (
) that incor-
porates station-level meteorological data, a digital elevation model, as well as other
spatialdatasets,inatypeof“expertsystem”designedtorepresenthowanexperienced
climatologist would create a climate map.
he histogram in Fig.
.
clearly shows a bimodal structure relating to the geog-
raphy of the state, a sharp mode to the right for the eastern plains, and a shorter,
broader mode indicating the lower temperatures of the mountain grid points.
he choice of bin width plays a critical role in the appearance and accuracy of the
histogram. heoretical analysis of the density histogram involves the multinomial
distributionandaTaylor'sseriesonthetruedistribution f ;seeScott(
)fordetails.
he variance of f
=
(
x
)
is dominated by a term of the form f
(
x
)
nh
j
,forx in B
j
,
Figure
.
.
Density histogram of average minimum winter temperature (degrees Celcius) over a grid of
locations in the US state of Colorado
