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October 13th, 2016, 06:38 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 622 Thanks: 85  I'm Looking For A Random Number Generator With Variable Probabilities Free Online Random Number Generator and Checker is a random number generator where every number in the range is equally likely to be selected on any trial unless you place restrictions on frequencies, but you can't tell it to make one number more likely than another number. Can somebody find a random number generator where you can input the probabilities for each number? It doesn't need to be able to handle 100 probabilities, but I would like if it could handle 20 probabilities.

October 13th, 2016, 09:35 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,195 Thanks: 1152 
probably the easiest way to do this is with a table. Suppose you have $N$ events each having $p_k$ probability of occuring. Further assume you have a random number generator that gives you uniform random real numbers [0,1]. Finally assume that you have some granularity of probability you are happy with so that you can write $p_k = \dfrac {m_k}{M}$ Now you create a table. The first $m_1$ entries point to the label for event 1 entries $m_1+1, m_1+m_2$ point to the label for event 2. entries $m_{n1}+1, m_{n1}+m_n$ point to the label for event $n$ As a quick example to make this clear. Suppose we have 5 events with a probability granularity of $\dfrac 1{10}$ Let's say the $m_k$'s are $\{1,3,2,1,3\}$ We make a $10$ element array as follows $\begin{bmatrix} 1\\ 2 \\ 2 \\ 2\\ 3 \\ 3 \\ 4 \\ 5 \\ 5 \\ 5 \end{bmatrix}$ You would get an RNG from your generator. Multiply it by 10 and round it to the nearest integer. Then use this an an index into the array and look up the corresponding event. Last edited by romsek; October 13th, 2016 at 10:25 PM. 
October 13th, 2016, 10:53 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,195 Thanks: 1152 
Note that if you have a closed form formula for the probability of event $k$ in terms of $k$ there are easier ways of generating the random numbers with that distribution. The table method is for when you just have a list of desired probabilities for your events w/o any particular formula. 
October 14th, 2016, 12:15 PM  #4 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 622 Thanks: 85 
Thank you. I'm working with www.random.org but I would still prefer if there was a random number generator that you could input your own probabilities for.

October 14th, 2016, 12:18 PM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 2,195 Thanks: 1152  Quote:
 
October 14th, 2016, 07:07 PM  #6 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 622 Thanks: 85  
October 14th, 2016, 07:51 PM  #7 
Senior Member Joined: Sep 2015 From: USA Posts: 2,195 Thanks: 1152 
were you going to use any software to do this? just do it by hand? 
October 16th, 2016, 08:16 AM  #8 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 622 Thanks: 85  

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generator, number, probabilities, random, variable 
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