Mathematica: Random numbers from arbitrary PDF

In summary, the conversation discusses how to generate a set of random numbers according to a specific distribution using Mathematica. The method involves modifying the RandomVariate function and utilizing inverse transform sampling or rejection sampling. This allows for the use of a custom distribution, such as the one given in the conversation.
  • #1
Niles
1,866
0
Hi

I want to generate a set of random numbers according to a specific distribution, namely given by
[tex]
f(v) \propto v^3\exp(-v^2 C)
[/tex]
where C is a constant. It is clear how to do it with a distribution already implemented in Mathematica, http://reference.wolfram.com/mathematica/tutorial/RandomNumberGeneration.html, but is there a way to do it with the one given by me above?


Niles.
 
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1. How do I generate random numbers from an arbitrary probability distribution using Mathematica?

To generate random numbers from an arbitrary probability distribution using Mathematica, you can use the function RandomVariate. This function takes two arguments - the probability distribution and the number of random numbers you want to generate. For example, if you want to generate 100 random numbers from a normal distribution with mean 0 and standard deviation 1, you can use the code RandomVariate[NormalDistribution[0,1], 100].

2. Can I specify a custom probability distribution for generating random numbers in Mathematica?

Yes, you can specify a custom probability distribution in Mathematica using the ProbabilityDistribution function. This function allows you to define the PDF (probability density function) for your desired distribution and then use it with the RandomVariate function to generate random numbers. You can also specify the domain and other parameters for your custom distribution.

3. How can I plot the histogram of the random numbers generated from an arbitrary PDF in Mathematica?

To plot the histogram of the random numbers generated from an arbitrary PDF in Mathematica, you can use the Histogram function. This function takes the list of random numbers as input and automatically creates a histogram with appropriate bin sizes. You can also specify the number of bins and other customization options for the histogram.

4. Is there a way to generate a sequence of random numbers from an arbitrary PDF in Mathematica?

Yes, you can generate a sequence of random numbers from an arbitrary PDF in Mathematica using the RandomVariate function. This function allows you to specify the number of random numbers you want to generate and also takes a seed value as an optional argument. This seed value ensures that the same sequence of random numbers is generated every time you run the code, making it reproducible.

5. Can I use the random numbers generated from an arbitrary PDF for statistical analysis in Mathematica?

Yes, you can use the random numbers generated from an arbitrary PDF for statistical analysis in Mathematica. You can use these numbers to perform various statistical tests, such as hypothesis testing and regression analysis, or to calculate descriptive statistics like mean, median, and standard deviation. You can also use these numbers for simulations and modeling in Mathematica.

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