Multiply two probability plots (CDF/PDF)
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- the distribution of a random variable that is the sum of independent A.Var7 and total_HOLT values
- the distribution of a random variable that is the product of independent A.Var7 and total_HOLT values
- the joint (bivariate) distribution of independent A.Var7 and total_HOLT values
- something else
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Hi @Deepayan Bhadra,
You mentioned, “How can I multiply these plots to convey a (qualitative) idea? “
Please see my response to your comments below.
My suggestion to achieve your goal of combining these two plots while maintaining clarity would be overlaying them in a single figure. This would allow you to visualize both the cumulative probabilities and the density of occurrences simultaneously. After analyzing your code, here is example code snippet to help you out.
% Generate some generic data for demonstration data = randn(1000, 1); % Normal distributed data
% Create CDF plot figure(); ax1 = subplot(1,1,1); cdfplot(data); hold on;
% Fit a normal distribution to the data pd = fitdist(data,'Normal');
% Generate x values for PDF x_values = linspace(min(data), max(data), 100); y_values = pdf(pd, x_values);
% Plot PDF on the same axes plot(x_values, y_values, 'r-', 'LineWidth', 2);
% Reverse x-axis and set log scale for y-axis ax1.XDir = 'reverse'; set(gca, 'YScale', 'log');
% Add legends and labels
legend('CDF', 'PDF');
xlabel('Value');
ylabel('Probability');
title('Combined CDF and PDF Plot');
hold off;
So, in above example code, I used randn(1000, 1) to create a sample dataset that follows a normal distribution. The cdfplot(data) function creates the cumulative distribution function plot. You will see that the example code fits a normal distribution to the data and calculates its PDF over a range of x-values. The hold on command allows you to overlay the PDF plot on top of the CDF plot in the same figure and the x-axis is reversed, for more information on this command, please refer to
https://www.mathworks.com/help/matlab/ref/hold.html#
and a logarithmic scale is applied to the y-axis for better visibility of both plots. Make sure when you visualize both plots together, see how the probability density (PDF) at each point contributes to the cumulative probability (CDF). This dual representation will help you understanding both local behavior (PDF) and global behavior (CDF) of your data distribution. Feel free to adjust line styles, colors, and markers according to your preferences for better visual distinction between CDF and PDF.
Please see attached.
If you have any further questions, please let me know.
11 个评论
Hi @Deepayan Bhadra,
You mentioned, “ I want one plot that conveys the diminishing trend. I don't even need to preserve them as probability plots.”
Please see my response to your comments below. Thanks for clarifying about your plot requirements. So, to combine the CDF and PDF into a single plot that effectively conveys a diminishing trend, you can normalize both the CDF and PDF so that they can be combined meaningfully. Then, multiply the standardized curves to visualize the interaction between them. Afterwards, create a single plot that represents this product. However, I did modify the above using generic data , please let me know if this resolves the issue.
% Generate some generic data for demonstration data = randn(1000, 1); % Normally distributed data
% Create CDF [values_cdf, x_cdf] = ecdf(data); cdf_standardized = values_cdf / max(values_cdf); % Standardize CDF
% Fit a normal distribution to the data for PDF pd = fitdist(data, 'Normal'); x_pdf = linspace(min(data), max(data), 100); pdf_values = pdf(pd, x_pdf); pdf_standardized = pdf_values / max(pdf_values); % Standardize PDF
% Multiply standardized CDF and PDF combined_curve = cdf_standardized .* interp1(x_pdf, pdf_standardized, x_cdf, 'linear', 'extrap');
% Plotting
figure();
plot(x_cdf, combined_curve, 'b-', 'LineWidth', 2);
hold on;
plot(x_cdf, cdf_standardized, 'r--', 'LineWidth', 1.5); % Original CDF for reference
plot(x_pdf, pdf_standardized, 'g--', 'LineWidth', 1.5); % Original PDF for reference
xlabel('Value');
ylabel('Combined Value');
title('Combined Diminishing Trend from CDF and PDF');
legend('Combined Curve', 'Standardized CDF', 'Standardized PDF');
set(gca, 'YScale', 'log'); % Log scale for better visibility
hold off;
Please see attached.
So, in the above code, you will find out that applying a logarithmic scale helps in visualizing trends better, especially when dealing with probabilities or densities that span several orders of magnitude. Standardizing both curves makes sure that they are comparable and can be meaningfully and the resulting combined curve visually represents how the likelihood of occurrence diminishes as you move away from the peak density. If you still have any further questions or need additional adjustments, please let me know!
I believe @Deepayan Bhadra's initial intention was to qualitatively interpret the meaning of the multiplication of the CDF and the PDF, or to derive the interpretation from the diminishing trend.
Your comments are duly noted and I do respect your opinion. Please let me briefly explain about my recent example code snippet provided, the process begins by generating normally distributed data and calculating both the CDF and PDF. Each function is then standardized to make sure they can be meaningfully combined. The key step involves multiplying the standardized CDF and PDF, which allows for a visual representation of their interaction. The resulting combined curve is plotted alongside the original standardized CDF and PDF for reference. This approach not only highlights the diminishing trend but also provides a qualitative interpretation of how the two distributions interact.
The use of a logarithmic scale enhances visibility, making it easier to observe the diminishing nature of the combined curve. This method effectively meets OP’s (@Deepayan Bhadra's) requirements by creating a single plot that conveys the desired trend without the need for preserving the original probability characteristics. Also, I would suggest that @Deepayan Bhadra should point out as well what part of the code not achieving her goal, so I can provide work around or share technical tips to help her out because the whole purpose of this Mathworks community is to share knowledge and help out OPs to achieve their goal which helps them not only understand the concept but also motivates them to lear more.
Hi @Deepayan Bhadra,
Glad to know your problem is resolved. For more information on ecdf function, please refer to
Hi @ Deepayan Bhadra,
After reviewing your comments second time, I do apologize for misunderstanding your comments. I have edited comments in above post. Your goal is to visualize how the values in vector a correspond to the ranges of values in vector b, specifically showing high probabilities within a certain range of b. Also, you want to represent discrete probabilities derived from two vectors, where:
- Vector a contains probability values.
- Vector b defines corresponding ranges.
In your given example, you are interested in showing that a value in vector b between -90 and -70 corresponds to a high probability from vector a. You already defined the data by representing them in two vectors:
a = [70, 23, 3, 0, 0, 0, 0, 0, 0, 0];
b = [-90, -80, -70, -60, -50, -40, -30, -20, -10, 0];
It will be helpful to normalize your probabilities so that they sum to 1 if you are treating them as probabilities. In this case:
total_probability = sum(a);
normalized_a = a / total_probability; % Normalize 'a'Then use a bar plot to represent the probabilities clearly. Here’s how you can implement this in MATLAB:
% Create the bar plot for probabilities
figure();
bar(b, normalized_a); % Use 'b' for x-axis and normalized probabilities for
y-axis
xlabel('Value (b)');
ylabel('Probability');
title('Discrete Probability Distribution');% Highlight the range of interest hold on; xline(-90,'r--','Start Range','LabelHorizontalAlignment','left'); xline(-70,'g--','End Range','LabelHorizontalAlignment','right');
% Customize y-axis limits if necessary ylim([0 max(normalized_a) * 1.1]);
% Add grid for better visibility grid on;
hold off;
As you can see in example code snippet, the bar function creates a bar plot where each bar represents the probability associated with each value in vector b. The xline function is used to add vertical lines at -90 and -70 to visually indicate the range of interest and normalization makes sure that your representation is consistent with probability principles. Finally, grid enhances readability by allowing viewers to gauge values more easily. This visualization will clearly show that values in vector a corresponding to b values between -90 and -70 are significantly higher than those outside this range. This can be crucial for interpreting data distributions or making decisions based on these probabilities.
Hope this answers your question. If you have further questions or need additional modifications, feel free to ask!
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