Hi Maximilian,
I understand that you are trying to perform a Monte Carlo sampling of 6 parameters, each with its own value range and probability distribution, to generate parameter combinations for sensitivity analysis in another program. You're looking for a way to sample these parameters based on their distributions to obtain specific combinations for your analysis.
To achieve this in MATLAB, you can use various functions depending on the type of distribution each parameter follows. For example, randn for normal distributions, rand for uniform distributions, and custom functions for triangular or other distributions. Here's a basic approach to generate 10 random parameter combinations from specified distributions:
- Define the distributions for each parameter. For simplicity, let's assume two parameters follow normal distributions (normrnd), two follow uniform distributions (unifrnd), and two follow triangular distributions (for which we'll define a custom sampling function).
- Sample from these distributions using Monte Carlo sampling. You'll generate a large number of combinations (e.g., 1 million) and then select a subset (e.g., 10) for your analysis.
Here is an example implementation in MATLAB:
triangularSample = @(min, mode, max, N) min + (max - min) .* sqrt(rand(N, 1) .* rand(N, 1));
param1 = normrnd(mu1, sigma1, [N, 1]);
param2 = normrnd(mu2, sigma2, [N, 1]);
param3 = unifrnd(a3, b3, [N, 1]);
param4 = unifrnd(a4, b4, [N, 1]);
param5 = triangularSample(1, 2, 3, N);
param6 = triangularSample(2, 4, 6, N);
params = [param1, param2, param3, param4, param5, param6];
idx = randperm(N, N_final);
selected_combinations = params(idx, :);
This code snippet provides a framework you can adapt based on the specific distributions and parameters of your analysis. Note that for the triangular distribution, you may need to implement a more appropriate sampling method or find a MATLAB function/library that supports it directly if the simple example provided does not suit your needs.
Refer to the following MathWorks documentation for more information on "randn", "rand", "normrnd" and "unifrnd" functions:
- "randn" function : https://in.mathworks.com/help/matlab/ref/randn.html
- "rand" function : https://in.mathworks.com/help/matlab/ref/rand.html
- "normrnd" function : https://in.mathworks.com/help/stats/normrnd.html
- "unifrnd" function : https://in.mathworks.com/help/stats/unifrnd.html
Hope this helps.
Regards,
Nipun