How can I use various colors to fill the area under a normal distribution curve?

Hi, I obtained a probability distribution for my data using the following syntax:

h = histfit(data);

and then:

pd = fitdist(data,'Normal');

I want to create a graph similar to Figure 1 using the mean and standard deviation values obtained from the histogram and fitted distribution.

In advance, I would like to express my gratitude for your assistance.

Figure 1:

Answer 1

[Star Strider]

Sure!

Try this —

x = linspace(1.5, 5, 250);
mu = 3.3;
s = 0.6;
y = normpdf(x, mu, s);

figure
plot(x, y)
hold on
Lv1 = (x>=mu) & (x<mu+s);
patch([x(Lv1) flip(x(Lv1))], [zeros(size(y(Lv1))) flip(y(Lv1))], 'g', 'EdgeColor','none')
Lv2 = (x>=mu+s) & (x<mu+2*s);
patch([x(Lv2) flip(x(Lv2))], [zeros(size(y(Lv2))) flip(y(Lv2))], 'y', 'EdgeColor','none')
Lv3 = (x>=mu+2*s) & (x<mu+3*s);
patch([x(Lv3) flip(x(Lv3))], [zeros(size(y(Lv3))) flip(y(Lv3))], 'r', 'EdgeColor','none')
hold off

If you want the text annotations as well, I can supply those, and the vertical lines, too.

.

[Navid]

Hi, Star Strider

I would greatly appreciate it if you could include the annotations and vertical lines in the code.

[Star Strider]

Unfortunately, the annotation arrows only work within the axes limits, as are any lines, so I could not plot them outside the axes. The best I can do for the others below the x-axis is to use text calls and improvise.

Try this —

x = linspace(1.5, 5, 250);
mu = 3.3;
s = 0.5;
y = normpdf(x, mu, s);
yann = interp1(x, y, ([0 1 2 3]*s+mu));

figure
plot(x, y)
hold on
Lv1 = (x>=mu) & (x<mu+s);
patch([x(Lv1) flip(x(Lv1))], [zeros(size(y(Lv1))) flip(y(Lv1))], 'g', 'EdgeColor','none')
Lv2 = (x>=mu+s) & (x<mu+2*s);
patch([x(Lv2) flip(x(Lv2))], [zeros(size(y(Lv2))) flip(y(Lv2))], 'y', 'EdgeColor','none')
Lv3 = (x>=mu+2*s) & (x<mu+3*s);
patch([x(Lv3) flip(x(Lv3))], [zeros(size(y(Lv3))) flip(y(Lv3))], 'r', 'EdgeColor','none')
plot([1;1]*([0 1 2 3]*s+mu), [zeros(1,4); yann], '-k')
hold off
Ax = gca;
opos = Ax.OuterPosition;
Ax.OuterPosition = opos+[0 +0.2 0 -0.2];
text(mu, 0, '\mu', 'Horiz','center', 'Vert','top', 'FontSize',12, 'FontWeight','bold', 'FontName','TimesRoman')
text(mu+[1 2 3]*s, yann(2:end), compose('%d\\sigma',[1 2 3]), 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

text(mu+s/2, -0.08, '1\sigma', 'FontWeight','bold', 'FontSize',10, 'Horiz','center', 'Vert','middle')
text(mu, -0.1, '\leftarrow——\rightarrow', 'FontWeight','bold', 'FontSize',10)
text(mu+s, -0.14, '2\sigma', 'FontWeight','bold', 'FontSize',10, 'Horiz','center', 'Vert','middle')
text(mu, -0.16, '\leftarrow———————\rightarrow', 'FontWeight','bold', 'FontSize',10)
text(mu+s*1.5, -0.20, '3\sigma', 'FontWeight','bold', 'FontSize',10, 'Horiz','center', 'Vert','middle')
text(mu, -0.22, '\leftarrow————————————\rightarrow', 'FontWeight','bold', 'FontSize',10)

This is my best effort. Make appropriate changes (for example 'FontWeight' and the others) to get the result you want. The lines extending the arrows from the ends to the centre are ‘em dashes’, char(0151) in the appropriate text calls.

The only way to use annotation arrows is to create them inside the axes limits, however that then requires drawing separate axis lines as well, so that everything is inside the original axes limits. That is not impossible, however it would require considerable time and effort.

.

[Navid]

Thank you so much for your time! However, there seems to be an error in the text syntax:

text(mu+[1 2 3]*s, yann(2:end), compose('%d\\sigma',[1 2 3]), 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

"Error using text: Invalid parameter/value pair arguments."

[Star Strider]

My pleasure!

Unfortunately, I no longer have access to R2016b, so I cannot determine exactly what the problem is. The compose function was introduced in R2016b, so it should not be the problem.

Since the text call above it seemed to work, the only thing I can think of is to break that one text call into three different text calls:

text(mu+s, yann(2), compose('%d\\sigma',1), 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

text(mu+2*s, yann(3), compose('%d\\sigma',2), 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

text(mu+3*s, yann(4), compose('%d\\sigma',3), 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

The others should not be a problem.

Another option is to remove the compose calls as well, since they are now no longer necessary:

text(mu+s, yann(2), '1\\sigma', 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

text(mu+2*s, yann(3), '2\\sigma', 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

text(mu+3*s, yann(4), '3\\sigma', 'FontName','TimesRoman', 'FontWeight','bold', 'Vert','bottom', 'Horiz','left', 'FontSize',12)

That should work.

I have an idea on how to correctly use the annotation arrows (instead of the text calls), however I will need to experiment with that. If I can devise an approach that works, I will post it here.

[Navid]

Thank you for your assistance. The second option was correctly implemented in my version. Thank you again.

[Star Strider]

As always, my pleasure!

Answer 2

[Angelo Yeo]

f = @(x, mu, sd) 1/(sd*sqrt(2*pi)) * exp(-1/2*((x-mu)/sd).^2);

x = linspace(1.5, 5, 1000);
mu = 3.25; sd = 0.5;

figure;
hold on;
x_zone1 = linspace(mu, mu+sd, 300);
x_zone2 = linspace(mu+sd, mu+2*sd, 300);
x_zone3 = linspace(mu+2*sd, mu+3*sd, 300);
area(x_zone1, f(x_zone1, mu, sd), 'FaceColor', 'g')
area(x_zone2, f(x_zone2, mu, sd), 'FaceColor', 'y')
area(x_zone3, f(x_zone3, mu, sd), 'FaceColor', 'r')
plot(x, f(x, mu, sd), 'color','k', 'linewidth', 2);

Answer 3

[Chunru]

data = randn(8192, 1);
h = histfit(data);

pd = fitdist(data,'Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = -0.00241653   [-0.0240676, 0.0192345]
    sigma =    0.999681   [0.984606, 1.01523]

figure;
x = linspace(-4*pd.sigma, 4*pd.sigma, 1001);
p = pdf(pd, x);
figure;
plot(x, p);
hold on
facecolor =["g", "y", "r"]

facecolor = 1×3 string array
    "g"    "y"    "r"

for i=1:3
    idx = (x >= (i-1)*pd.sigma) & (x < i*pd.sigma);
    area(x(idx), p(idx), FaceColor=facecolor(i))
end

[Navid]

Hello Chunru,

Thank you for your time. Unfortunately, there was an error related to the area syntax.

area(x(idx), p(idx), FaceColor=facecolor(i))

Error: The expression to the left of the equals sign is not a valid target for an assignment.

[Chunru]

It seems that you are using older version of matlab. Use the following name-value syntax for older version matlab.

area(x(idx), p(idx), 'FaceColor', facecolor(i))

[Navid]

Dear Chunru

I wanted to express my gratitude for the assistance you provided. I successfully modified your code and achieved my desired outcome thanks to your guidance. I appreciate your help.

mu = pd.mu; sd = pd.sigma;
x = linspace(mu-4*pd.sigma,mu+4*pd.sigma,1001);
p = pdf(pd,x);
figure;
plot(x,p);
hold on
facecolor=['g','y','r'];
for i=1:3
    idx = (x>= mu+(i-1)*pd.sigma)&(x<mu+i*pd.sigma);
    area(x(idx), p(idx), 'FaceColor', facecolor(i))
end