Cells
Classes of histogram plots
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Mandatory | List of arithmetical expressions |
Objects | Cells Default Values |
---|---|
plot::Histogram2d | [7 ] |
Cells
determines the number and position
of the classes used in a histogram.
Cells
accepts either a single positive integer
(or, equivalently, a list of one positive integer) or a list of cells
given as ranges or lists of two elements.
A single integer n in
the specification Cells = n
or Cells =
[n]
is interpreted as “subdivide the range of data
into n cells
of equal size.”
The number n can be animated. In this case, n may be a symbolic expression of the animation parameter.
The cells may be specified directly as in Cells = [[a_{1},
b_{1}], [a_{2}, b_{2}],
…]
or Cells = [a_1..b_1, a_2..b_2, Symbol::dots]
.
The i-th cell is the semi-open interval , i.e., a datum x is tallied into the i-th cell if a_{i} < x ≤ b_{i} is satisfied.
The cell boundaries must satisfy a_{1} < b_{1} ≤ a_{2} < b_{2} ≤ a_{3} < …. In most applications, b_{1} = a_{2}, b_{2} = a_{3} etc. is appropriate.
If giving cells directly, the leftmost border may be -
infinity
and the rightmost border may be infinity
. These rectangles
will then be adjusted according to the average widths of the other
rectangles for display purposes.
With the attribute CellsClosed
= Left
,
the cells [a_1..b_1, a_2..b_2, Symbol::dots]
are
interpreted as the semi-open intervals .
We create a sample of 1000 data points and plot a histogram of them:
X := stats::fRandom(100, 10): data := [X() $ i = 1..1000]: plot(plot::Histogram2d(data))
The shape of the distribution becomes much better visible when we increase the number of cells:
plot(plot::Histogram2d(data, Cells = 40))
plot(plot::Histogram2d(data, Cells = [40], Area = 1), plot::Function2d(stats::fPDF(100,10)(x), x = 0 .. 5, Color = RGB::Black))
With cells of different widths, setting Area
to a positive value
is highly recommended, to still have the histogram follow the probability
distribution:
cells := stats::equiprobableCells(50, stats::fQuantile(100, 10))
plot(plot::Histogram2d(data, Cells = cells)):
plot(plot::Histogram2d(data, Cells = cells, Area = 1), plot::Function2d(stats::fPDF(100, 10)(x), x = 0 .. 5, Color = RGB::Black))