Weighted Random Number Generator in Javascript - Stack Overflow

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I am using the following code to generate a random number:

function getRandomInt (min, max) {
    return Math.floor((Math.random() * (max - min + 1)) + min;
}

What I want to do is add a weighting that favours the numbers at the lower end of the range.

I thought about maybe trying to multiply the numbers by 1/cosine.

Would this work and does anyone know how I might go about it?

Many thanks!

I am using the following code to generate a random number:

function getRandomInt (min, max) {
    return Math.floor((Math.random() * (max - min + 1)) + min;
}

What I want to do is add a weighting that favours the numbers at the lower end of the range.

I thought about maybe trying to multiply the numbers by 1/cosine.

Would this work and does anyone know how I might go about it?

Many thanks!

• javascript

Share Improve this question Follow edited Jun 1, 2015 at 2:16 Amit Verma 41.2k2121 gold badges9797 silver badges118118 bronze badges asked Dec 14, 2013 at 18:14 user3102815user3102815 7111 silver badge55 bronze badges 5

• possible duplicate of Generate A Weighted Random Number – Felix Kling Commented Dec 14, 2013 at 18:16
• if you want a cosine distribution you have to apply the inverse cosine, that means arccos(x) with x being your uniform random sample – Marian Theisen Commented Dec 14, 2013 at 18:16
• 1 what distribution do you want? – Stephen Thomas Commented Dec 14, 2013 at 19:01
• I am not sure how best to explain this. Imagine a logarithmic curve that goes from 0-1. If the RNG returns a value of 0.5 I want to apply a weighting to being it down to say, 0.2. If 1 is returned, I would like to keep the number up at around 1, and similarly 0 with 0. – user3102815 Commented Dec 14, 2013 at 19:24
• Ask a new question. Your "edit" has pletely changed the question. And ask ot on math exchange. – chiliNUT Commented Dec 14, 2013 at 21:04

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2 Answers 2

Sorted by: Reset to default 12

First Solution

You need a function which contains the points (0, 0) and (1, 1). For instance: x^n when n > 0

Math.pow(1, n) === 1

And

Math.pow(0, n) === 0

Therefore, you would just change n depending on how you want the weighting to work.

• When n = 1 : y === x
• When n > 1 : y <= x
• When 0 < n < 1 : y >= x

So, if you want lower values to be favored over higher values, simply use n > 1.

var weighted = Math.pow(Math.random(), 2);

Then you can scale the result as usual.

var scaled = Math.floor(weighted * (max - min + 1)) + min;

Other Functions

Likewise, you could use any continuous function which contains the points (0, 0), (1, 1), and has range and domain of [0, 1].

Sine

y = sin(xπ/2)

Cosine

y = 1 - cos(xπ/2)

EDIT: there was a type in the final formula, log(2+log(x)) is incorrect it should have been log(1+log(x))+1, its fixed now.

If you are using logarithmic weighting, using something like

var x = Math.random();
var weighted = x * Math.log(1+x);

would make 0.5 weigh in at around 0.2, but 1 would only weigh in at around 0.69.

Using this

var x = Math.random();
var weighted = x * Math.log(2 + Math.log(x));

would allow 1 to weigh in at 1. So bine them, and this

var x = Math.random();
var weighted = (x <= 0.5) ? x * Math.log(1 + x) : x * Math.log(1 + Math.log(x))+1;

should do the trick

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