How to determine and plot a probability density function?

I have a vector (8760 x 1) with the hourly electricity prices in a network and another vector (8760 x 1) with the quantity of electricity sold in each hour. I want to know how to get and plot the probability density function of that data. As an example, here are the first eleven elements of each vector:

    Prices = [44.2200; 45.1300; 46.2300; 47.9100; 49.5700; 48.6900; 47.2000; 46.5100; 46.5200; 51.5900; 59.0700];
    SoldElectricity = [0; 0; 0; 2.1255; 1.9807; 1.8474; 1.0561; 0; 0; 0.3586; 6.0510];

And I want to get a plot like this as a result:

(In the image three different sold electricity vectors were plotted, in my case, I only need to plot one) Any help would be appreciated, thanks!

Answer 1

[Jeff Miller]

The discretize function will do most of the job. You may have to play around with it a bit, but something like this should work:

bins = 43.5:1:60.5;  % define some bins that cover the range of interest
assignments = discretize(Prices,bins);  % get a vector telling you which bin each price is in

% compute how much was sold in each bin
bintotals = zeros(size(bins));
for ibin=1:numel(bins)
   bintotals(ibin) = sum(SoldElectricity(assignments==ibin));
end

binprobs = bintotals / sum(bintotals);  % compute the proportion of the total in each bin

plot(bins,binprobs);

Answer 2

[jonas]

You can use the following function form the statistics toolbox

ksdensity(SoldElectricity)

Note that the function outputs a non-parameteric estimate, which may not be desirable. A purely empirical pdf can be designed using histograms

histogram(SoldElectricity,'Normalization','pdf','displaystyle','stairs','binmethod','integers')

See attachment for results

[Leon Gutierrez Guerrero]

Thank you Jonas. The thing is that that solution does not relate both vectors. What I want to do is to determinate the probability density of the vector ‘Prices’ taking into account the quantity of MW (vector ‘SoldElectricity’) sold at each price. Any idea how to do that?

[Jeff Miller]

The plot that you said you wanted (i.e., with Probability Density on the vertical axis) does not relate two vectors either. Can you give a better example of the plot you want--something showing probability density as a function of both prices and quantity? It sounds like you really want a bivariate density.

[jonas]

As Jeff Miller has already commented, that makes little sense and is not what you asked in the original submission. Please clarify what your desired output is.

[Leon Gutierrez Guerrero]

Sorry for the misunderstanding, I’m probably confusing concepts. To clarify, I will explain what I need to do with an example I worked out in excel using the vectors mentioned in my first submission: The values of the vector ‘Prices’ goes from $44.22 to $59.07, so I defined 16 bins as follows:

Then I included a column with the total electricity sold at each price range (according to vector ’SoldElectricity’):

And finally, I divided each value of the second column by the total amount of energy sold (13.41926667MWh) to obtain the probability:

The plot of the probability vs price is this:

I did this manually in excel, but I need to do it automatically in Matlab for 8760 values. Thanks for your help!

[israt fatema]

Hi Leon, did you find the solution for your problem? Would you mind sharing your solution please?

Thank you.