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

Question

Navid 2023-11-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2052857-how-can-i-use-various-colors-to-fill-the-area-under-a-normal-distribution-curve

评论： Star Strider 2023-11-28

采纳的回答： Star Strider

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:

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Answer 1

Star Strider 2023-11-28

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在 MATLAB Online 中打开

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.

.

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Star Strider 2023-11-28

在 MATLAB Online 中打开

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.

.

Star Strider 2023-11-28

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 2023-11-28

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

Star Strider 2023-11-28

As always, my pleasure!

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Answer 2

Angelo Yeo 2023-11-28

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2052857-how-can-i-use-various-colors-to-fill-the-area-under-a-normal-distribution-curve#answer_1361042

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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);

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Answer 3

Chunru 2023-11-28

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https://ww2.mathworks.cn/matlabcentral/answers/2052857-how-can-i-use-various-colors-to-fill-the-area-under-a-normal-distribution-curve#answer_1361047

编辑：Chunru 2023-11-28

在 MATLAB Online 中打开

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

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Chunru 2023-11-28

在 MATLAB Online 中打开

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 2023-11-28

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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