Generating a distribution around a parameter using monte carlo simulation.

Hello, I wish for someone to help me explain (with a code example) how i can generate a distribution around a value (say 0.007695) using Monte Carlo simulation. I understand that I might first need to generate set of random variables using 0.007695 as control.

I will be grateful to get a response. Am just a basic user of matlab

Answer 1

[Jeff Miller]

The Gaussian distribution has two parameters, mean and standard deviation. Once you decide on values for those, it is easy to generate a sample of random numbers. For example:

mu = 0.0076;     % the mean you asked for
sigma = 0.0003;  % adjust to make the distribution as wide as you want.
samplesize = 1000;
randvals = randn(samplesize,1)*sigma + mu;
histogram(randvals);

[Gumps]

Hello Jeff, your explanation was quite useful.Thank you. Please do you know how I can transform this Gaussian distribution into an indicator transform? The reason why I need the transform is to put some numbers into certain ranges and then go in to use their probabilities for my work.

[Jeff Miller]

I don't know what you mean by an "indicator transform". Can you give an example?

[Gumps]

Hello Jeff, Thank you for your usual quick response. By indicator transform I mean that since the values (variables) are much (say 100), I want to assign a number or ID to each range and then plot the distribution.

Example; assuming our random numbers are from 0 to 1, I want to assign numbers from 0 to 0.01 as i1, 0.01 to 0.02 as i2 etc and then replot the distribution again (if possible to show the ranges and the indicators in the plot if possible)

[Jeff Miller]

Look at the documentation for histcounts. I think you can get those numbers from something like

edges = 0:0.01:1;
[~,~,bins] = histcounts(rands,edges);

[Gumps]

ok. lemme see. Thanks alot.

[Gumps]

Hello Jeff, I have just looked at the histcounts. Not clear enough

Answer 2

[possibility]

Generally, the way it works is you already possess the data samples (say millions of them) and find the histogram of the data (frequency of the values that appears in the data). After that, you pick the optimum distribution model (Gaussian, Laplacian, chi-square, etc.) that fits best to your samples.

But, if you're trying to ask "how to generate samples from a distribution with a given statistical parameter (for ex: mean)", that would have meaningful answers.

One example,

randn

command generates samples from a gaussian distribution. Or

rand

generates samples from a uniform distribution. Just type

help rand

for details.

Hope that helps.

[Gumps]

Hello Yavuz, thank you for quick response. Actually, I just have a simple value of say 0.0076 and I want to generate random samples around it and after which I can now define these samples with a gaussian distribution taking my known value as the mean... I would really appreciate if you can be of great help. Thank you