How can I choose an element from a vector according to its probability ?

I want to select an angle according to the probability. I executed the code below its show me the only FIRST option (only 10 even when I change the probability value its show me the same option). Thank in advance for any help

t=0.1;Ang_1 = [10 20 30 45 80];% this vector of options
for i:1:1
    prob = (exp((1/t)*1.2*10^-5))./(exp((1/t)*1.2*10^-4)) % this is probability could be changable each eteration
    select = Ang_1(find(rand<cumsum(prob),1)) % select angle according to "prob"
end

Answer 1

[Steven Lord]

t=0.1;Ang_1 = [10 20 30 45 80];% this vector of options

Since your for loop had invalid syntax and you don't use what I suspect you intended to be the loop variable (i) inside the loop I commented it out.

%for i:1:1
    prob = (exp((1/t)*1.2*10^-5))./(exp((1/t)*1.2*10^-4)) % this is probability could be changable each eteration

prob = 0.9989

    select = Ang_1(find(rand<cumsum(prob),1)) % select angle according to "prob"

select = 10

%end

Since prob is a scalar, cumsum(prob) is just prob itself. So that find call will return either 1 or [] depending on whether rand generated a number less than prob or not.

If you had a vector of probabilities, like this which uses the value in Ang_1 as the relative frequency of the value:

probabilities = [0 cumsum(Ang_1)./sum(Ang_1)]

probabilities = 1×6

0 0.0541 0.1622 0.3243 0.5676 1.0000

then you could use discretize to generate your list.

x = rand(10, 1);
values = discretize(x, probabilities, Ang_1);

Another way to generate these values is as categories.

categories = discretize(x, probabilities, 'categorical');

Let's summarize the results in a table.

results = table(x, values, categories)

results = 10×3 table
       x       values        categories     
    _______    ______    ___________________

    0.66418      80      [0.56757, 1]       
    0.33411      45      [0.32432, 0.56757) 
    0.22314      30      [0.16216, 0.32432) 
    0.76124      80      [0.56757, 1]       
    0.33686      45      [0.32432, 0.56757) 
    0.90657      80      [0.56757, 1]       
    0.13988      20      [0.054054, 0.16216)
    0.49154      45      [0.32432, 0.56757) 
    0.51494      45      [0.32432, 0.56757) 
    0.83691      80      [0.56757, 1]       

[omar th]

@Steven Lord First Thanks for your response. Actually that prop is scalar due to measured via the mentioned equation BUT its changing in each iteration of for loop. Now I want choose ONLY one of these options according to prob in each iteration of for loop ?? Thanks for your

for j=1:100
    for i=1:1
        % here the prob is changable in each iteration
    end
end

[Steven Lord]

Build your equivalent of the probabilities vector I used in my example in the loop. Once you've done that you can discretize after the loop.