Matlab estimate PDF from random variable X

[Dustinsfl]

How do I estimate the pdf from a random variable \(X\) where \(X = U_1 - U_2\) and \(U_i\) are uniform random variables?

In the code below, I used unifrnd(-5, 5, 1000, 1) which generated a 1000x1 vector of uniform random number between -5 and 5.

How do I estimate the PDF for X?

rng;
X = unifrnd(-5, 5, 1000, 1) - unifrnd(-5, 5, 1000, 1);
bincenters = (-5:0.5:5);
bins = length(bincenters);

h = zeros(bins, 1);              %  pre-allocating h

for i = 1:length(X)
    for k = 1:bins
        if X(i) > bincenters(k) - 0.5/2 && X(i) <= bincenters(k) + 0.5/2
            h(k, 1) = h(k, 1) + 1;
        end
    end
end

pxest = h/(1000*0.5);

bar(bincenters, pxest)

 

[zzephod]

How do I estimate the pdf from a random variable \(X\) where \(X = U_1 - U_2\) and \(U_i\) are uniform random variables?

In the code below, I used unifrnd(-5, 5, 1000, 1) which generated a 1000x1 vector of uniform random number between -5 and 5.

How do I estimate the PDF for X?

rng;
X = unifrnd(-5, 5, 1000, 1) - unifrnd(-5, 5, 1000, 1);
bincenters = (-5:0.5:5);
bins = length(bincenters);

h = zeros(bins, 1);              %  pre-allocating h

for i = 1:length(X)
    for k = 1:bins
        if X(i) > bincenters(k) - 0.5/2 && X(i) <= bincenters(k) + 0.5/2
            h(k, 1) = h(k, 1) + 1;
        end
    end
end

pxest = h/(1000*0.5);

bar(bincenters, pxest)

What are you really trying to do?

There is no need to "estimate" this distribution you know it, it is the symmetric triangular distribution with support (-10,10).

Otherwise google "kernel density estimation", or "matlab ksdensity".

.

 

[Dustinsfl]

What are you really trying to do?

There is no need to "estimate" this distribution you know it, it is the symmetric triangular distribution with support (-10,10).

Otherwise google "kernel density estimation", or "matlab ksdensity".

.

I just doing a problem out of a book on stochastic processes.

 

[zzephod]

I just doing a problem out of a book on stochastic processes.

What is the exact wording of the problem.

.

 

[alphy]

To estimate the PDF for X, we can use the approach of binning the data and counting the number of observations falling within each bin. In this case, we have two uniform random variables, U1 and U2, and we want to estimate the PDF for their difference, X = U1 - U2.

First, we generate a large number of random values for U1 and U2 using the unifrnd function in MATLAB. In this code, we generate 1000 values for each variable, but this can be adjusted as needed.

Next, we create a vector of bin centers, which will serve as the boundaries for our bins. In this code, we use a bin width of 0.5, but this can also be adjusted based on the range of values for X.

We then create a loop to go through each observation of X and count the number of values falling within each bin. This is done by comparing each value of X to the bin boundaries and incrementing the corresponding bin count.

Finally, we divide the bin counts by the total number of observations (1000) and the bin width (0.5) to obtain an estimate of the PDF for X. This is then plotted as a bar graph using the bar function in MATLAB.

It is important to note that this is just one method for estimating the PDF from a random variable in MATLAB. Other methods, such as kernel density estimation, can also be used depending on the specific needs of the analysis.