Finding the common area between the distribution of empirical data and log normal distribution

Hello,

I have plotted a ks density plot for my data. In addition I have plotted normally used distributions above it I want to see how common area they have between them.

fullfile = [pathname, filename];

sampledata = readtable(fullfile);

index_m=sampledata.Type=="M" ;

data_m = sampledata.CycleTime(index_m,:);

index_r=sampledata.Type=="R";

data_r = sampledata.CycleTime(index_r,:);

% Fit a log-normal distribution to the data

mu_ln = mean(log(data_m));

sigma_ln = std(log(data_m));

% Fit a log-logistic distribution to the data

paramLogLogistic = fitdist(data_m, 'loglogistic');

alpha = paramLogLogistic.ParameterValues(1);

beta = paramLogLogistic.ParameterValues(2);

% Generate a range of values for the x-axis

x = linspace(0.3, 7, 1000);

% Compute the log-normal PDF

pdf_ln = lognpdf(x, mu_ln, sigma_ln);

% Compute the log-logistic PDF

pdf_loglogistic = pdf(paramLogLogistic, x); % Renamed from "pdf" to "pdf_loglogistic"

xticks_values = [0 1 2 3 4 5 6 7]; % Adjust as needed

yticks_values = [0 0.2 0.4 0.6 0.8 1]; % Adjust as needed

% Create a KS density plot

figure;

subplot(2,1,1)

ksdensity(data_m);

hold on;

plot(x, pdf_ln, 'r', 'LineWidth', 2);

plot(x, pdf_loglogistic, 'g', 'LineWidth', 2);

title('M');

xlabel('Cycletime (mins)');

ylabel('Density');

legend('Empirical Data', 'Log-Normal Distribution', 'Log-Logistic Distribution');

xlim([0 7]);

xticks(xticks_values);

yticks(yticks_values);

hold off;

index_r=sampledata.Type=="R";

data_r = sampledata.CycleTime(index_r,:);

% Fit a log-normal distribution to the data

mu_ln = mean(log(data_r));

sigma_ln = std(log(data_r));

% Fit a log-logistic distribution to the data

paramLogLogistic = fitdist(data_r, 'loglogistic');

alpha = paramLogLogistic.ParameterValues(1);

beta = paramLogLogistic.ParameterValues(2);

% Generate a range of values for the x-axis

x = linspace(0.3, 7, 1000);

% Compute the log-normal PDF

pdf_ln = lognpdf(x, mu_ln, sigma_ln);

% Compute the log-logistic PDF

pdf_loglogistic = pdf(paramLogLogistic, x); % Renamed from "pdf" to "pdf_loglogistic"

subplot(2,1,2)

ksdensity(data_r);

hold on;

plot(x, pdf_ln, 'r', 'LineWidth', 2);

plot(x, pdf_loglogistic, 'g', 'LineWidth', 2);

title('R');

xlabel('Cycletime (mins)');

ylabel('Density');

legend('Empirical Data', 'Log-Normal Distribution', 'Log-Logistic Distribution');

xlim([0 7]);

xticks(xticks_values);

yticks(yticks_values);

hold off;

[dpb]

Please format your code with Code button (LH icon in CODE section) and attach necessary datafile(s) to be able to see/run your code.

Then, what, specifically, is the problem you're having?

[Muhammad Tariq]

I got the answer from Balaji. I do not have problem with the code. Just wanted to see the difference between the area of two distributions.

Thankyou!

Answer 1

[Balaji]

Hi Muhammad

I understand that you are trying to find the are between two functions that you have defined. I suggest you use the ‘trapz’ function for the same.

You can refer to the following code:

% Find the absolute difference between the two curves 
diff_curve = abs(pdf_ln - pdf_loglogistic); 

% Calculate the area between the curves using the trapz function 
area = trapz(x, diff_curve); 

For more information on ‘trapz’ function isuggest you refer to the following link:

https://www.mathworks.com/help/matlab/ref/trapz.html

Hope this helps

Thanks

Balaji

[Muhammad Tariq]

Thankyou Balaji,

It works!