Normal probability plot
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Syntax
normplot(x)
normplot(ax,x)
h = normplot(___)
Description
example
normplot(x)
creates a normal probability plot comparing the distribution of the data in x
to the normal distribution.
normplot
plots each data point in x
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.
normplot(ax,x)
adds a normal probability plot into the axes specified by ax
.
example
h = normplot(___)
returns graphics handles corresponding to the plotted lines, using any of the previous syntaxes.
Examples
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Generate a Normal Probability Plot
Open Live Script
Generate random sample data from a normal distribution with mu = 10
and sigma = 1
.
rng default; % For reproducibilityx = 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.
Assess Normality Using a Normal Probability Plot
Open Live Script
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 reproducibilityx1 = 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.
figuresubplot(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.
figuresubplot(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')
Adjust Normal Probability Plot Line Properties
Open Live Script
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 reproducibilityx = [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.
figureh = normplot(x)
h = 6x1 Line array: Line Line Line Line Line Line
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;
Input Arguments
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x
— Sample data
numeric vector | numeric matrix
Sample data, specified as a numeric vector or numeric matrix. normplot
displays each value in x
using the symbol '+'
. If x
is a matrix, then normplot
displays a separate line for each column of x
.
Data Types: single
| double
ax
— Target axes
Axes
object | UIAxes
object
Target axes, specified as an Axes
object or a UIAxes
object. normplot
adds an additional plot into the axes specified by ax
. For details, see Axes Properties and UIAxes Properties.
Use gca to return the current axes for the current figure.
Output Arguments
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h
— Graphics handles for line objects
vector of Line
graphics handles
Graphics handles for line objects, returned as a vector of Line
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 x, normplot
returns three handles:
The line representing the data points.
normplot
represents each data point inx
using plus sign ('+'
) markers.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 values of
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.
Algorithms
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.
Alternative Functionality
You can use the probplot function to create a probability plot. The probplot
function enables you to indicate censored data and specify the distribution for a probability plot.
Version History
Introduced before R2006a
See Also
probplot | cdfplot | wblplot | ecdf
Topics
- Distribution Plots
- Hypothesis Testing
- Normal Distribution
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