A histogram is fundamentally a summary of the frequency of discrete
outcomes (bins), so in a sense the answer to your question is no (in
the limit, with small enough bins, all of them will have zero counts
except those actually observed in your sample, which probably isn't
useful). However, if what you really want is a probability
distribution over the possible values, that can be defined
continuously by selecting a model (e.g., a Gaussian, but there are
many others) and then fitting it to the observed values. The fitted
model can then be evaluated at any possible value v to give you P(v).
Cheers,
Kiri
On Nov 29, 2009, at 2:44 PM, Yakir Gagnon wrote:
Hi everybody,
Hope someone can help me or point me to the right direction:
I have some function f(x) with some predefined domain (say zero to
one: 0 <= x <= 1). I want to calculate the function that describes
its histogram.
So if I choose say 100 discrete values for x (all within its
domain), I get 100 values for y (y = f(x)). I choose some bin size
and get my histogram that describes y's distribution.
I can then try and choose a billion discrete values and some smaller
bin size and get a "better" approximation of that histogram.
What I wonder is:
Is there no formal way to analytically calculate what the histogram
is for the independent variable of a given function?
Thanks tons!
Yakir L. Gagnon, PhD student
The Lund Vision Group
Tel +46 (046) 222 93 40
Cell +46 (073) 753 63 54
Fax +46 (046) 222 44 25
http://www.lu.se/o.o.i.s/7758
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