Php random number generate - php

Question

My task:
Generate random numbers between 1 and 20, to 1 decimal place.
However my issue as simple as mt_rand. I want most of the numbers generated to be lower around 0.5 - 4.5 with the occasional number being between 4.5-10 and very rarely say once every 12-20 hours being between 10-20.
I've been using the following but have no idea where to go from. I am a very basic self-taught programmer.
$min = 1;
$max = 20;
$suisse_interest = mt_rand ($min*10, $max*10) / 10
Maybe if I briefly explain why I want this it may help..
I own an online game and want to add 3 "banks" with each bank generating different interests each hour. Most of the time I want it low, but sometimes higher and very rarely very high (15-20%).
With the above code the random number goes too high to often.
Any help with this is greatly appreciated!

Answer 1

You need an exponential calculation. If you use a function similar to the following function, the probability for low numbers increases. Of course you need to adapt the numbers a bit to provide an output suiting your needs.
$i = 0;
while($i<30) {
$i++;
$rand = mt_rand(0, 7000) / 100; // 0.0 ~ 70.0
// This is the most important line:
$output = round( 20*(pow(0.95,$rand)) , 1);
echo "$output ";
}
Sample output:
1.8 4.3 2.6 5.5 3.7 15.5 1.6 0.6 0.6 1.6 5.8
1.3 6.1 3.2 0.8 1.7 14.7 7.9 1.3 10.3 5.5 12.6
1.5 8.4 1.5 0.9 13.3 5.8 7.5 1.7
As you see, mostly smaller number are printed.
The probability to get 20 is around 1.4% in my code whereas the probability to get a number smaller than 5 is around 78%

Answer 2

Try this.The probability to 1.0~4.5 is around 96%, 4.5~10.0 is around 2%, and 10.0~20.0 is around 2%.
<?php
// 1.0~4.5 96%
// 4.5~10.0 2%
// 10.0~20.0 2%
function fun() {
$num = mt_rand(1, 100);
if ($num > 0 && $num <= 96) {
$return = mt_rand(10, 45) / 10; // 96%
} else if ($num > 96 && $num <= 98) {
$return = mt_rand(45, 100) / 10; // 2%
} else {
$return = mt_rand(100, 200) / 10; // 2%
}
return sprintf("%01.1f",$return);
}
echo fun();
?>

Answer 3

This is not a PHP-specific problem.
What you need is a non-linear probability law, that you can then implement in PHP.
If you want something centered around an average value, the ideal would be a gaussian aka normal distribution, but computing it requires various complicated tricks, most of them being optimized for rapid generation at the cost of increasing complexity.
If you generate only a few values each hour, performance will not be an issue.
A reasonable approximation would be to sum 3 or 4 random variables, taking advantage of the central limit theorem.
Summing random values between 0 and twice your middle rate will create an approximation of a gaussian centered around your middle value.
You can then clamp values inferior to the middle point if you don't want low rates. The net result would be 50% chances of getting middle rate and a steadily decreasing chance to get up to twice that value.
An increasing number of sums will "narrow" the curve, making it less likely to get a high value.
for instance:
define ("INTEREST_MEAN", 10);
define ("INTEREST_SPREAD", 5);
function random_interest ()
{
$res = 0;
for ($i = 0 ; $i != INTEREST_SPREAD ; $i++) $res += mt_rand(0, 2*INTEREST_MEAN);
$res /= INTEREST_SPREAD; // normalize the sum to get a mean-centered result
$res = max ($res, INTEREST_MEAN); // clamp lower values
}