Gaussian Curve Plotting Issues

Hey everyone, I am working on a normal distribution to better understand the random choice dataset I am working with. The current gaussian curve is very wrong and I am not sure why. Basically, in a group of 10,000 individuals there is a 1.3% chance they will be placed in population A, and a 98.7% chance an individual is placed in population B. I am mainly concerned with population A, as that is the population of interest. The random assignment is ran 100 times, and the values are placed in empty arrays RunSumA1 and RunSumB1.

Here is the current code and graph:

options = ['A', 'B'];

%Empty vectors for value storage
RunSumA1=[];
RunSumB1=[];

ListOneProbability=0.013;
ListTwoProbability=0.987;
totalRuns = 100;

%Storage loop from function
for k=1:totalRuns
   [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability); 
end

%Converting to Column Vector
RunSumA1 = RunSumA1';

%Average, STD, Normal PDF
mu = mean(RunSumA1);
sigma = std(RunSumA1);
y = normpdf(RunSumA1, mu, sigma);

%Plot
plot(RunSumA1, y)

%Random choice function
function [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability)
    tempA1 = 0;
    tempB1 = 0;
    
    for j=1:10000
        newChoice = randsample(options, 1,true, [ListOneProbability,ListTwoProbability]);
        
        if newChoice == 'A'
          tempA1=tempA1+1;
        else
          tempB1=tempB1+1;
        end
        
    end
    
    RunSumA1=[RunSumA1,tempA1];
    RunSumB1=[RunSumB1,tempB1];
end

Answer 1

[the cyclist]

Can you be more specific what you mean by "the current gaussian curve is very wrong"? Do you mean with the lines connecting all over the place? If you just plot points rather than lines, then you see the nice smooth curve:

options = ['A', 'B'];

%Empty vectors for value storage
RunSumA1=[];
RunSumB1=[];

ListOneProbability=0.013;
ListTwoProbability=0.987;
totalRuns = 100;

%Storage loop from function
for k=1:totalRuns
   [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability); 
end

%Converting to Column Vector
RunSumA1 = RunSumA1';

%Average, STD, Normal PDF
mu = mean(RunSumA1);
sigma = std(RunSumA1);
y = normpdf(RunSumA1, mu, sigma);

%Plot
plot(RunSumA1, y, '.') % Changed this line to plot only the points

%Random choice function
function [RunSumA1,RunSumB1]= my_sorter(RunSumA1,RunSumB1,options,ListOneProbability,ListTwoProbability)
    tempA1 = 0;
    tempB1 = 0;
    
    for j=1:5000 % I made the smaller, since it would not time out on the Answers forum
        newChoice = randsample(options, 1,true, [ListOneProbability,ListTwoProbability]);
        
        if newChoice == 'A'
          tempA1=tempA1+1;
        else
          tempB1=tempB1+1;
        end
        
    end
    
    RunSumA1=[RunSumA1,tempA1];
    RunSumB1=[RunSumB1,tempB1];
end

Is that it? Or is there some other problem?

[Nicholas Fuller]

Yeah that was pretty much it. Kicking myself for not thinking of just using points to plot it. I was wondering if there was anything wrong with the code since it produced the interconnected lines rather than one smooth curve.

Answer 2

[Alan Stevens]

If you have 10000 individuals with a probability of 0.013 of being in group A, you would expect your curve to peak close to 130 individuals on average. Perhaps you want something like the following:

Npop = 10000;
probA = 0.013;

Ntrials = 100;  % 
A = zeros(Ntrials, 1);
B = zeros(Ntrials, 1);
for trial = 1:Ntrials
   r = rand(Npop,1);
   ir = find(r<=probA);
   A(trial) = numel(ir);
   B(trial) = Npop - A(trial);
end

mu = mean(A);
sigma = std(A);
disp([mu, sigma])

  128.4800   10.9420

lo = 80;
hi = 180;
x = linspace(lo,hi,100);
y = exp(-0.5*((x-mu)/sigma).^2)/(sigma*sqrt(2*pi));

plot(x,y)
xlabel('Numbers in group A')
ylabel('frequency')
grid