Biased integer

[TimWolla]

biasedInteger allows generating an integer that is biased by a given function.

See #304

See this example data:

Number	unbiased	linearLow	linearHigh	sqrt	square
1	9857	19016	1007	3222	84
2	10032	17000	2931	5715	717
3	9966	14977	4928	7538	1846
4	9914	13015	7033	8872	3645
5	10099	11080	9145	9915	6095
6	9800	9012	11001	11234	9138
7	9987	6860	12936	11906	12800
8	10096	5053	15047	13160	17019
9	10026	2945	16919	13775	21512
10	10223	1042	19053	14663	27144
Loop iterations:	100000	200217	199822	150115	299345
Loop iterations (percent)	100.00%	200.22%	199.82%	150.12%	299.34%

Loop iterations are the number of times the contents of the loop were executed, 100000 is perfect, no values were discarded.

For even more fascination see this sqrt distribution of a higher number range 😄

[fzaninotto]

I don't understand why you do this. Why isn't the following sufficient?

public function biasedInteger($min, $max, $function)
{
    $randMax = mt_getrandmax();
    return floor($function(mt_rand(0,$randMax) / $randMax) * ($max - $min + 1) + $min);
}

[TimWolla]

It would make creation of the “weighting” functions less intuitive. My method directly maps the distribution onto a graph and one can easily see: “Oh, that value is higher, the number is more likely to pop out”.

I cannot think of any function that would generate a linearLow distribution using your method on top of my head.

[fzaninotto]

how about:

function linearLow(x)
{
   return x / 2;
}

Your approach is really not fast enough because of the loop.

[TimWolla]

return x / 2;

This would create all the lower half with equal probability and none of the higher half (so it is essentially the same as numberBetween($min, $max / 2).

[fzaninotto]

Sorry, I shouldn't do maths after midnight :)

But anyway, I think power and root functions already deal with 90% of the required biases.

[TimWolla]

Well, even powers are completely unintuitive with your suggestion. What distribution would you expect when using pow($x, 4);? Are the low, the medium or the high numbers favored? Think a moment about it.

I would say: The high ones, but after thinking about it one will see that in fact the lower numbers are favored!

Therefore I will not change the actual algorithm, unless the distribution stays (roughly) the same. And the numbers show that depending on the chosen function the biased generator is between 33% and 16% of the speed of numberBetween (see loop iterations percent), there are worse generators (e.g. numerify, which generates each digit independently).

If I could convince you I will happily fix the test failures and rename the function and whatnot, but if you still think that the algorithm is too slow then you may close the pull request.

[fzaninotto]

After thinking again about it, I agree with you approach. Do you have time to make the requested changes to make it mergeable?

[TimWolla]

After thinking again about it, I agree with you approach. Do you have time to make the requested changes to make it mergeable?

I'll try to take a look at it before end of the week.

[TimWolla]

@fzaninotto The remaining issues should be fixed.

[TimWolla]

As a note: That tests fail is not my fault.

[fzaninotto]

Thanks!

[jayenne]

Hi, would this function be able to have return a number biased towards a 3rd number using a function?

e.g.. I want to generate users to a demographic with a min, max and mean age with a function like sqrt, gauss etc...

min = 0, max = 100, mean = 33, function= ? returns a "falloff curve" around the mean rather than one end or the other?

[christhofer]

Hi, what other values we can use in 3rd parameter?
Please update the documentation with more example, e.g how to make it biased for lower values, for middle values, or to use our own function maybe.

Tried $faker->biasedNumberBetween(1, 50, 'linearLow'),
I got error

call_user_func() expects parameter 1 to be a valid callback, function 'linearLow' not found or invalid function name
at D:\Projects\PHP\api.tss\vendor\fzaninotto\faker\src\Faker\Provider\Biased.php:27
    23|     {
    24|         do {
    25|             $x = mt_rand() / mt_getrandmax();
    26|             $y = mt_rand() / (mt_getrandmax() + 1);
  > 27|         } while (call_user_func($function, $x) < $y);
    28| 
    29|         return (int) floor($x * ($max - $min + 1) + $min);
    30|     }
    31|