Generating Biased Random Number

I want to select a number in the interval of [0,1,2,3,....,22,23], but by a bias,

for example I want to select the 21 by the probability of 20% and 23 by %10, and the others by equal probability? what should I do?

[Walter Roberson]

Do you have the statistics toolbox ?

Answer 1

[the cyclist]

If you have the Statistics Toolbox, then I recommend using the randsample() command to do this type of sampling.

>> doc randsample

for details.

Answer 2

[Ryan G]

I'm no statistician, so I bet there's a better way but you can try this without stats toolbox:

Setup an index for each number in the vector and use randi to select the actual value. For example (3 numbers for ease of example).

   myVec = [1 1 1 2 2 3 3 3 3 3]; % 1 is 30%, 2 is 20% and 3 is 50% chance
   selectRand = randi(10,1); %choose the index
   finalValue = myVec(selectRand) %select that number from the original vector

Since randi is uniformally distributed this should do the job. You could use:

   randi(100,1);

to select the percentages with integer precision from 0 to 100%. You would need to figure out the best way to create myVec for your values.

Answer 3

[Daniel Shub]

What about

y = rand;
if y < .1
  x = 23;
elseif y < .3
  x = 22
else
  x = randi(21);
end

Answer 4

[Matt Fig]

Without the stats toolbox:

A = 0:23;  % The given array.

% Now lets sample it.
N = .5e5;  % This many samples..
At = [0:20 22];

for ii = N:-1:1
    B = rand;
    if B>=.7 && B<.9
        F(ii) = 21;
    elseif B>=.9
        F(ii) = 23;
    else
        F(ii) = At(randperm(22,1));
    end    
end

% Check that it worked.
hist(F,A) % should show even bars for all but two
sum(F==23)/length(F) % should be close to .1
sum(F==21)/length(F) % should be close to .2

.

.

.

EDIT

Here is a vectorized version of the above code:

A = 0:23;  % The given array.
At = [0:20 22];
N = 100000;  % This many samples..
F = rand(1,N);
F(F>=.7 & F<.9) = 21;
F(F>=.9 & F<1) = 23;
F(F<=1) = At(randi(22,1,sum(F<=1)));

% Check that it worked.
hist(F,A) % should show even bars for all but two
sum(F==23)/length(F) % should be close to .1
sum(F==21)/length(F) % should be close to .2

Answer 5

[Walter Roberson]

N = 1000;  %how many to generate
SampleVector = 0:23;   %does not need to be ordered or consecutive or integer
UsualProbability = (1 - 0.20 - 0.10) ./ (24-2);
ProbabilityVector = repmat(UsualProbability,1,24);
ProbabilityVector(22) = 0.10;
ProbabilityVector(24) = 0.20;

slots = [0, cumsum(ProbabilityVector)];
[counts, slotidx] = histc(rand(1,N), slots);
randsamples = SampleVector(slotidx);