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I have a vector with 50 elements. These are values of a random variable. I have represented the data as Histogram[RandomVariable1Histogram]. However, I need to obtain a bigger sample from said histogram, about 1000 values. If I were working with a known distribution, lets say a Gamma, I could simply write

nsim = 1000;
newValues = 
 RandomVariate[GammaDistribution[\[Alpha]0, \[Beta]0], nsim]; 

However, since I am currently dealing with an unknown random variable, I don't know how to sample said histogram. My only idea is to use HistogramDistribution and somehow put the output inside of RandomVariate. However, I am not very happy with this since it requires the calculation of a probability density function. Is there a better way of obtaining a sample of a random variable of which only a histogram is available?

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You may do this using "SmoothKernelDistribution".

Here is a simple example. We first create some data from a Normal Distribution:

d = RandomVariate[NormalDistribution[], 100];

Then we get a smooth distribution from this data:

dist= SmoothKernelDistribution[d];

We can now test the outcome by sampling from this distribution and see if it is approximately normal:

rv = RandomVariate[dist, 1000];
Mean[rv]
Variance[rv]
Histogram[rv]

enter image description here

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  • $\begingroup$ Thanks for your answer. I have read the documentation of SmoothKernelDistribution and attempted empiricPDF = SmoothKernelDistribution[RandomVariable1Histogram] and d = RandomVariate[empiricPDF, 1000]; it seems to work if I write Histogram[d] $\endgroup$ Nov 25 at 11:25
  • $\begingroup$ The answer needs to be modified. What is dist above? $\endgroup$
    – Asim
    Nov 25 at 15:31
  • $\begingroup$ This is exactly what one would do if the raw data is available. But I read that the OP only has the histogram (bins and bin counts). $\endgroup$
    – JimB
    Nov 25 at 16:30
  • $\begingroup$ From a histogram one can always create some data with multiple entries. $\endgroup$ Nov 25 at 16:40
  • $\begingroup$ @Asim. Thanks, it looks like I copied the wrong line. I corrected it. $\endgroup$ Nov 25 at 16:41
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This is precisely what RandomChoice does: choosing numbers according to weights. For example, if your histogram is

hist = {99, 217, 1026, 3};

then you can draw a random number from $\{1,2,3,4\}$ that is distributed similarly with

RandomChoice[hist -> Range[Length[hist]]]

or you can draw $10^6$ numbers simultaneously with

RandomChoice[hist -> Range[Length[hist]], 10^6]
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