本文介绍了两个 beta 分布的乘积的处理方法,对大家解决问题具有一定的参考价值,需要的朋友们下面随着小编来一起学习吧!
问题描述
假设我有两个随机变量:
Say I have two random variables:
X ~ Beta(α1,β1)
X ~ Beta(α1,β1)
Y ~ Beta(α2,β2)
Y ~ Beta(α2,β2)
我想计算 Z = XY(随机变量的乘积)的分布
I would like to compute distribution of Z = XY (the product of the random variables)
使用 scipy,我可以获得单个 Beta 版的 pdf:
With scipy, I can get the pdf of a single Beta with:
from scipy.stats import beta rv = beta(a, b) x = np.linspace(start=0, stop=1, num=200) my_pdf = rv.pdf(x)但是两个 Beta 的乘积呢?我可以分析吗?(Python/Julia/R 解决方案很好).
But what about the product of two Betas? Can I do this analytically? (Python/Julia/R solutions are fine).
推荐答案对于分析解决方案,请查看 这篇论文和这个答案.
For an analytical solution, have a look at this paper and this answer.
R
set.seed(1) # for reproducability n <- 100000 # number of random variables # first beta distribution a1 <- 0.5 b1 <- 0.9 X <- rbeta(n, a1, b1) # second beta distribution a2 <- 0.9 b2 <- 0.5 Y <- rbeta(n, a2, b2) # calculate product Z <- X * Y # Have a look at the distributions plot(density(Z), col = "red", main = "Distributions") lines(density(X), lty = 2) lines(density(Y), lty = 2)更多推荐
两个 beta 分布的乘积
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