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How to generate random data that is not normal (With a Given Distribution) ?
For instance, how to generate data for a weighted dice (also known as weighted or crooked die) with the following weights:
- Number 1: 1
- Number 2: 3
- Number 3: 1
- Number 4: 2
- Number 5: 1
- Number 6: 4
Algorithm
Weighted list
- Make a weighted list:
{ 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 6, 6 }
- Generate the list index randomly in order to get your element in the list. The list index is then a random number that is 0 or greater and is less than the length of the list (ie sum of the weights)
<math> \text{random list index} = (\text{random number between 0 and 1}) * 12 </math>
- Pick your element in the list corresponding to this random index
Sum of weights
- Calculate the sum of all the weights:
<math> 1 + 3 + 1 + 2 + 1 + 4 = 12 </math>
- Pick a random number that is 0 or greater and is less than the sum of the weights
- Go through the items one at a time, subtracting their weight from your random number, until you get the item where the random number is less than that item's weight