Tag: numbers

I originally posted this on StackOverflow but was requested to post it here instead as it relates to optimization/performance of the code rather than a specific problem.

TL;DR: Get-Random produces an even distribution of numbers where every number in the pool has an even chance of appearing. I’m looking for a way to generate random numbers where every individual number appears with a frequency that I myself specify.

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If I run

for($i=1;$i -le 1000;$i++){
    Get-Random -Minimum 0 -Maximum 10
}

I get a very evenly distributed count for each number (roughly 100 for each number between 0 and 9). Using Get-Random allows me to get a random number every time but on average, every individual result will appear roughly an equal amount of times. I want to decide the frequency for how often any specific number appears, and then generate random numbers that fit that distribution. As an example:

Number   Probability
0        10
1        11
2        19
3        12
4        3
5        10
6        6
7        7
8        4
9        18

I’m looking for a way to use the above list to randomly generate a number between 0 to 9, but with the probability of each individual number appearing using the Probability column.

My very hard-coded and not so generic solution so far is that I thought of doing something like adding a cumulative percentage column:

Number   Probability   CumulativeProbability
0        10            10
1        11            21
2        19            40
3        12            52
4        3             55
5        10            65
6        6             71
7        7             78
8        4             82
9        18            100

And from here, run the object through a filter. Something like:

$RandomNumber = Get-Random -Minimum 0 -Maximum 100
$MyProbabilityObject | Where-Object {$RandomNumber -ge $_.CumulativeProbability}

This gives me all numbers with a lower Cumulative probability than the random number. Let’s say the $RandomNumber was 42, that would result in:

Number   Probability   CumulativeProbability
0        10            10
1        11            21
2        19            40

From here, I could pipe the result to

Select-Object CumulativeProbability | Measure-Object -Property CumulativeProbability -Maximum 

Which gives me the highest value, and then use that column as a reference to find the number with

Where-Object {$_.CumulativeProbability -eq $TheNumberIGetAbove}

While this kinda works, it feels like I’m doing several laps around a problem that should be easier and more straightforward to solve. Are there any better ways of generating random numbers that fit a distribution you specify yourself instead of using an even distribution such as Get-Random?