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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