Question

Just wondering what type of algorithm this is,
or if there is an easier/more efficient way to go about this:

Say we are given a certain probability density, say

prob[] = {.1, .15, .25, .05, .45}

Group 1 – 10%
Group 2 – 15%
Group 3 – 25%
Group 4 – 5%
Group 5 – 45%

and a random number, (0,1),
ran = .853234

Insert into one of the 5 groups

if (ran <=prob[0]) selection = 1;  
else if (ran <= prob[0]+prob[1]) selection = 2;  
...
else if (ran <= prob[0]+prob[1]+...+prob[4]) selection = 5;  

I am not very well-versed on random number generation

Answer 1

What you are essentially doing here is inverting the cumulative distribution function. Let F be the CDF of a random variable X with a given distribution, then it is defined as F(x) == P[X <= x].

The very useful thing here, is that if you generate a uniform random variable U between 0 and 1, then

P[F^-1(U) <= x] == P[U <= F(x)] == F(x) == P[X <= x]

which means that F^-1(U) will have the same distribution as X!

Of course this is only possible if you can invert the CDF, but in your case Fis a piecewise function (like a staircase), and your algorithm determines, for a given uniform value, at which step this value is met. Your algorithm is therefore perfectly correct.

However, you could improve it if you have a lot of random numbers to generate: first generate the CDF table, which in your case would be

CDF[] = {.1, .25, .5, .55, 1.}

then for each generated uniform number between 0 and 1, simply perform a dichotomy on the CDF table to retriver the corresponding index.