normplot

Generate random sample data from a normal distribution with mu = 10 and sigma = 1.

rng default;  % For reproducibility
x = normrnd(10,1,25,1);

Create a normal probability plot of the sample data.

figure;
normplot(x)

The plot indicates that the data follows a normal distribution.

Generate 50 random numbers from each of four different distributions: A standard normal distribution; a Student's-t distribution with five degrees of freedom (a "fat-tailed" distribution); a set of Pearson random numbers with mu equal to 0, sigma equal to 1, skewness equal to 0.5, and kurtosis equal to 3 (a "right-skewed" distribution); and a set of Pearson random numbers with mu equal to 0, sigma equal to 1, skewness equal to -0.5, and kurtosis equal to 3 (a "left-skewed" distribution).

rng(11)  % For reproducibility
x1 = normrnd(0,1,[50,1]);
x2 = trnd(5,[50,1]);
x3 = pearsrnd(0,1,0.5,3,[50,1]);
x4 = pearsrnd(0,1,-0.5,3,[50,1]);

Plot four histograms on the same figure for a visual comparison of the pdf of each distribution.

figure
subplot(2,2,1)
histogram(x1,10)
title('Normal')
axis([-4,4,0,15])

subplot(2,2,2)
histogram(x2,10)
title('Fat Tails')
axis([-4,4,0,15])

subplot(2,2,3)
histogram(x3,10)
title('Right-Skewed')
axis([-4,4,0,15])

subplot(2,2,4)
histogram(x4,10)
title('Left-Skewed')
axis([-4,4,0,15])

The histograms show how each sample differs from the normal distribution.

Create a normal probability plot for each sample.

figure
subplot(2,2,1)
normplot(x1)
title('Normal')

subplot(2,2,2)
normplot(x2)
title('Fat Tails')

subplot(2,2,3)
normplot(x3)
title('Right-Skewed')

subplot(2,2,4)
normplot(x4)
title('Left-Skewed')

Create a 50-by-2 matrix containing 50 random numbers from each of two different distributions: A standard normal distribution in column 1, and a set of Pearson random numbers with mu equal to 0, sigma equal to 1, skewness equal to 0.5, and kurtosis equal to 3 (a "right-skewed" distribution) in column 2.

rng default  % For reproducibility
x = [normrnd(0,1,[50,1]) pearsrnd(0,1,0.5,3,[50,1])];

Create a normal probability plot for both samples on the same figure. Return the plot line graphic handles.

figure
h = normplot(x)

h = 
  6x1 Line array:

  Line    (Data)
  Line    (Data)
  Line    (Reference Mid)
  Line    (Reference Mid)
  Line    (Reference Ends)
  Line    (Reference Ends)

legend({'Normal','Right-Skewed'},'Location','southeast')

The handles h(1) and h(2) correspond to the data points for the normal and skewed distributions, respectively. The handles h(3) and h(4) correspond to the second and third quartile line fit to the sample data. The handles h(5) and h(6) correspond to the extrapolated line that extends to the minimum and maximum of each set of sample data.

To illustrate, increase the line width of the second and third quartile line for the normally distributed data sample (represented by h(3)) to 2.

h(3).LineWidth = 2;
h(4).LineWidth = 2;