# Is there a function to create the P-P plot in Matlab, to compare two cumulative distribution functions against each other?

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From Wikipedia: "In statistics, a P–P plot (probability–probability plot or percent–percent plot or P value plot) is a probability plot for assessing how closely two data sets agree, or for assessing how closely a dataset fits a particular model. It works by plotting the two cumulative distribution functions against each other; if they are similar, the data will appear to be nearly a straight line. This behavior is similar to that of the more widely used Q–Q plot, with which it is often confused."

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### Accepted Answer

Torsten
on 6 Sep 2024

Moved: Torsten
on 6 Sep 2024

rng default; % for reproducibility

a = 0;

b = 100;

nb = 50;

% Create two log-normal distributed random datasets, "x" and "y'

% (but we can use any randomly distributed data)

x = (b-a).*round(lognrnd(1,1,1000,1)) + a;

y = (b-a).*round(lognrnd(0.88,1.1,1000,1)) + a;

[F,t1] = ecdf(x);

[t1,ia] = unique(t1,'Stable');

F = F(ia);

[G,t2] = ecdf(y);

[t2,ia] = unique(t2,'Stable');

G = G(ia);

teval = unique(sort([t1;t2]));

Feval = interp1(t1,F,teval);

Geval = interp1(t2,G,teval);

hold on

plot(Feval,Geval,'o')

plot(0:1,0:1,'-','color','k')

hold off

grid on

##### 3 Comments

Torsten
on 6 Sep 2024

Edited: Torsten
on 6 Sep 2024

% Modified Rahul solution

% inputs

rng default;

a = 0;

b = 100;

nb = 50;

x = (b-a).*round(lognrnd(1,1,1000,1)) + a;

y = (b-a).*round(lognrnd(0.88,1.1,1000,1)) + a;

[f1, x1] = ecdf(x);

[f2, x2] = ecdf(y);

[x1_unique, ia1, ~] = unique(x1);

f1_unique = f1(ia1);

[x2_unique, ia2, ~] = unique(x2);

f2_unique = f2(ia2);

f1_interp = interp1(x1_unique, f1_unique, union(x1_unique,x2_unique));

f2_interp = interp1(x2_unique, f2_unique, union(x1_unique,x2_unique));

hold on

plot(f1_interp, f2_interp, 'o');

plot(0:1,0:1,'-','color','k')

hold off

grid on

### More Answers (1)

Rahul
on 6 Sep 2024

Edited: Rahul
on 7 Sep 2024

Hi Sim,

I understand that you’re trying to generate aPP (Probability-Probability) plot of two datasets, where a pp plot is made by plotting the fraction failing (CDF) of one distribution vs the fraction failing (CDF) of another distribution.

To generate this plot we simply plot the CDF of one distribution vs the CDF of another distribution. If the distributions are very similar, the points will lie on the 45 degree diagonal. Any deviation from this diagonal indicates that one distribution is leading or lagging the other.

Below is the reference code for your understanding:

1. Define Your Data

Assuming two datasets of unirform random distribution, ‘data1’ and ‘data2’, which you want to compare using a P–P plot.

data1 = randn(100, 1); % Example data set 1

data2 = randn(100, 1); % Example data set 2

2. Compute the Cumulative Distribution Functions (CDFs)

You need to calculate the empirical CDFs of both datasets, for which you can use the ‘ecdf’ function, and futher interpolate the CDF values to match the percentiles of the other dataset.

% Compute CDFs for data1

[f1, x1] = ecdf(data1);

% Compute CDFs for data2

[f2, x2] = ecdf(data2);

% Ensure x1 and x2 are unique and sorted

[x1_unique, ia1, ~] = unique(x1);

f1_unique = f1(ia1);

[x2_unique, ia2, ~] = unique(x2);

f2_unique = f2(ia2);

% Interpolate CDFs

f1_interp = interp1(x1_unique, f1_unique, x2_unique, 'linear', 'extrap');

f2_interp = interp1(x2_unique, f2_unique, x1_unique, 'linear', 'extrap');

3. Create the P–P Plot

After aligning CDF values from both datasets, you can plot them against each other.

figure;

plot(f1_interp, f2_interp, 'o');

xlabel('CDF of data1');

ylabel('CDF of data2');

title('P–P Plot');

hold on;

xline = [min(f1_interp), max(f1_interp)];

yline = xline;

% Plot the 45-degree line

plot(xline, yline, 'r--', 'LineWidth', 2);

axis equal;

grid on;

- Normalization: Make sure your datasets are appropriately scaled or normalized if they are not in the same range.
- Handling NaNs or Infinities: Ensure your data does not contain NaNs or infinities, which can affect interpolation and plotting.

For more information regarding usage of ‘cdf’ function, refer to the documentation link mentioned below:

https://www.mathworks.com/help/stats/prob.normaldistribution.cdf.html

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