Normal probability plot
normplot( creates a normal probability plot
comparing the distribution of the data in
x to the normal
normplot plots each data point in
using plus sign (
'+') markers and draws two reference lines that
represent the theoretical distribution. A solid reference line connects the first
and third quartiles of the data, and a dashed reference line extends the solid line
to the ends of the data. If the sample data has a normal distribution, then the data
points appear along the reference line. A distribution other than normal introduces
curvature in the data plot.
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.
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 Line Line Line Line Line
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;
x— Sample data
Sample data, specified as a numeric vector or numeric matrix.
displays each value in
x using the symbol
x is a matrix, then
normplot displays a
separate line for each column of
h— Graphics handles for line objects
Graphics handles for line objects, returned as a vector of
graphics handles. Graphics handles are unique identifiers that you can use to query and
modify the properties of a specific line on the plot. For each column of
normplot returns three
The line representing the data points.
represents each data point in
x using plus sign
The line joining the first and third quartiles of each column of
x, represented as a solid line.
The extrapolation of the quartile line, extended to the minimum and maximum
x, represented as a dashed line.
To view and set properties of line objects, use dot notation. For information on using
dot notation, see Access Property Values. For
information on the
Line properties that you can set, see Line Properties.
normplot matches the quantiles of sample data to the quantiles of
a normal distribution. The sample data is sorted and plotted on the x-axis. The y-axis
represents the quantiles of the normal distribution, converted into probability values.
Therefore, the y-axis scaling is not linear.
Where the x-axis value is the ith sorted value from a sample of size N, the y-axis value is the midpoint between evaluation points of the empirical cumulative distribution function of the data. The midpoint is equal to .
normplot superimposes a reference line to assess the linearity of
the plot. The line goes through the first and third quartiles of the data.
You can use the
probplot function to create a probability
probplot function enables you to indicate censored data
and specify the distribution for a probability plot.