如何在 Matlab 中绘制均匀随机变量的 pdf

Question

x 和 y 具有均匀分布，我想在 Matlab 中绘制 z 的 pdf。

x ~ U(0,1)

y ~ U(0,1)

Z = (-2.ln(x))^0.5  * cos(2.pi.y)

我该怎么做？

Answer 1

推导 Z 的分布需要一些时间，尽管从 CDF such as P(Z<=z) then condition on X=x or Y=y. Not clear which will be easiest path to eventually get the explicit CDF or PDF. But P(Z<=z|X = x) or P(Z<=z|Y = y) seems best approach. Cross Validated (https://stats.stackexchange.com/) is probably the best place to get the analytical derivation in progress here.

开始可能是最简单的

根据经验，这很容易获得并且样本量足够大，它应该适用于许多应用程序。

N = 5000;
X = rand(N,1);
Y = rand(N,1);
Z = cos(2*pi*Y).*(-2*log(X)).^2;

figure, hold on, box on
histogram(Z,'Normalization','pdf')

如果您想将 Z 视为 (X,Y) 的函数，这些可能会有所帮助。

n = 100;
x = linspace(0,1,n);
y = linspace(0,1,n);
[X,Y] = meshgrid(x,y);
Z = cos(2*pi*Y).*(-2*log(X)).^2;

等高线图不是很有用

但是表面图显示了更多基于 (X,Y) 的情况

如何在 Matlab 中绘制均匀随机变量的 pdf

How to plot pdf of uniform random variables in Matlab

matlab

probability-density