在 Matlab 中生成三角分布

发布于 2025-01-04 19:14:48 字数 629 浏览 4 评论 0原文

我尝试在 Matlab 中生成三角概率分布，但没有成功。我使用了 http://en.wikipedia.org/wiki/Triangle_distribution 中的公式。

n = 10000000;

a = 0.2;
b = 0.7;
c = 0.5;

u = sqrt(rand(n, 1));

x = zeros(n, 1);
for i = 1:n
    U = u(i);
    if U < (c-a)/(b-a)
        X = a + sqrt(U*(b-a)*(c-a));
    else
        X = b - sqrt((1-U)*(b-a)*(b-c));        
    end
    x(i) = X;
end

hist(x, 100);

直方图看起来像这样：

在此处输入图像描述

对我来说看起来不太像三角形。有什么问题吗？我是否滥用了rand(n)？

原文

I have attempted to generate a triangular probability distribution in Matlab, but was not successful. I used the formula at http://en.wikipedia.org/wiki/Triangular_distribution.

n = 10000000;

a = 0.2;
b = 0.7;
c = 0.5;

u = sqrt(rand(n, 1));

x = zeros(n, 1);
for i = 1:n
    U = u(i);
    if U < (c-a)/(b-a)
        X = a + sqrt(U*(b-a)*(c-a));
    else
        X = b - sqrt((1-U)*(b-a)*(b-c));        
    end
    x(i) = X;
end

hist(x, 100);

The histogram looks like so:

enter image description here

Doesn't look like much of a triangle to me. What's the problem? Am I abusing rand(n)?

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沙沙粒小 2025-01-11 19:14:48

您可以将两个均匀分布相加，分布图进行卷积，然后得到三角形分布。

易于理解的示例：掷两个骰子，每个动作具有均匀分布，产生 1-6 的数字，组合动作具有三角形分布，产生数字 2-12

编辑：最小工作示例：

a=randint(10000,1,10);
b=randint(10000,1,10);

c=a+b;

hist(c,max(c)-min(c)+1)

edit2：查看您的再次脚本。它可以工作，但你犯了一个错误：

u = sqrt(rand(n, 1));

应该是

u = rand(n, 1);

~~edit3: optimization code~~

n = 10000000; a = 0.2; b = 0.7; c = 0.5; u = rand(n, 1); x = zeros(n, 1); idx = find(u < (c-a)/(b-a)); x(idx) = a + sqrt(u(idx)*(b-a)*(c-a)); idx =setdiff(1:n,idx); x(idx) = b - sqrt((1-u(idx))*(b-a)*(b-c)); hist(x, 100);

you can add up two uniform distributions, the distribution graphs convolve, and you get a triangular distribution.

easy-to-understand example: rolling two dice, each action has uniform distribution to result in a number from 1-6, combined action has triangular distribution to result in a number 2-12

edit: minimal working example:

a=randint(10000,1,10);
b=randint(10000,1,10);

c=a+b;

hist(c,max(c)-min(c)+1)

edit2: looked in your script again. It's working but you've made one mistake:

u = sqrt(rand(n, 1));

should be

u = rand(n, 1);

~~edit3: optimized code~~

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隔岸观火 2025-01-11 19:14:48

此示例使用 makedist() 和 < a href="https://www.mathworks.com/help/stats/prob.normaldistribution.pdf.html" rel="nofollow noreferrer">pdf() 命令。

a = 2; m = 7; b = 10;
N = 50000;                             % Number of samples
pd = makedist('Triangular',a,m,b);     % Create probability distribution object

T = random(pd,N,1);                    % Generate samples from distribution

三角分布，下限 a = 7，众数 m = 10，上限 b = 10。

% Plot PDF & Compare with Generated Sample
X = (a-2:.1:b+2);

figure, hold on, box on
histogram(T,'Normalization','pdf') % Note normalization-pdf option name-value pair
title([num2str(N) ' Samples'])
plot(X,pdf(pd,X),'r--','LineWidth',1.8)
legend('Empirical Density','Theoretical Density','Location','northwest')

MATLAB 引入了 makedist()。需要统计工具箱。

参考：
三角分布

This example uses the makedist() and pdf() commands.

a = 2; m = 7; b = 10;
N = 50000;                             % Number of samples
pd = makedist('Triangular',a,m,b);     % Create probability distribution object

T = random(pd,N,1);                    % Generate samples from distribution

Triangular Distribution with lowerbound a = 7, mode m = 10, and upperbound b = 10.

% Plot PDF & Compare with Generated Sample
X = (a-2:.1:b+2);

figure, hold on, box on
histogram(T,'Normalization','pdf') % Note normalization-pdf option name-value pair
title([num2str(N) ' Samples'])
plot(X,pdf(pd,X),'r--','LineWidth',1.8)
legend('Empirical Density','Theoretical Density','Location','northwest')

MATLAB introduced makedist() in R2013a. Requires Stats toolbox.

Reference:
Triangular Distribution

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