Model Monte Carlo Simulation

Hi, I want to use monte carlo simulation for my model uncertainty analysis. Model equation is y= (a x b x c) / d. For this equation a and b are measureable deterministic variables and change day by day. c and d are stochastic variables. c has uniform distribution interval of [25,35] and d has uniform distribuiton interval of [35,70].

5 day measurements are shown below.

day 1 a= 7 b= 8

day 2 a= 9 b= 12

day 3 a= 14 b= 15

day 4 a= 18 b= 19

day 5 a= 5 b= 4

How can ı draw histogram and calculate mean,standard deviation for output (y) by using 10 000 samples for each day. Thank you for your help.

Answer 1

[Parag]

Hi, please see the below MATLAB code to draw histogram and calculate mean, standard deviation for output (y) by using 10 000 samples each day.

% Deterministic variables for each day 
a_values = [8, 9, 7, 6, 5]; % a for day 1 to 5 
b_values = [8, 12, 15, 10, 4]; % b for day 1 to 5 
% Stochastic variable ranges 
c_min = 25; c_max = 35; % Uniform distribution for c 
d_min = 35; d_max = 70; % Uniform distribution for d 
% Number of Monte Carlo samples 
num_samples = 10000; 
% Initialize storage for results 
means = zeros(1, 5); % Mean of y for each day 
std_devs = zeros(1, 5); % Standard deviation of y for each day 
% Loop through each day 
for day = 1:5 
    % Get deterministic variables for the day 
    a = a_values(day); 
    b = b_values(day);  
    % Generate random samples for c and d 
    c = c_min + (c_max - c_min) * rand(num_samples, 1); 
    d = d_min + (d_max - d_min) * rand(num_samples, 1); 
    % Compute y for all samples 
    y = (a * b * c) ./ d; 
    % Compute mean and standard deviation of y 
    means(day) = mean(y); 
    std_devs(day) = std(y); 
    % Plot histogram of y 
    figure; 
    histogram(y, 50, 'Normalization', 'pdf'); % 50 bins, normalized as PDF 
    title(['Day ', num2str(day), ' Histogram of y']); 
    xlabel('y'); 
    ylabel('Probability Density'); 
end 

% Display mean and standard deviation for each day 
disp('Mean of y for each day:'); 
disp(means); 

disp('Standard deviation of y for each day:'); 
disp(std_devs); 

If you would like to know more about Monte Carlo Simulation, you can refer to following documentation: https://www.mathworks.com/discovery/monte-carlo-simulation.html