为什么 scipy.norm.pdf 有时会给出 PDF >1?如何纠正? [英] Why does scipy.norm.pdf sometimes give PDF > 1? How to correct it?

问题描述

给定高斯(正态)随机变量的均值和方差，我想计算其概率密度函数 (PDF).

我参考了这篇文章:

怎么可能有 200% 的概率得到平均值 1.075?我在这里误解了什么吗?有什么办法可以纠正吗?

解决方案

这不是错误.这也不是错误的结果.某个特定点的概率密度函数值不会给你概率；它衡量分布围绕该值的密集.对于连续随机变量，给定点的概率为零.代替 p(X = x)，我们计算 2 个点之间的概率 p(x1 并且它等于低于该概率密度的区域功能.概率密度函数的值可以很好地在1以上，甚至可以接近无穷大.

Given mean and variance of a Gaussian (normal) random variable, I would like to compute its probability density function (PDF).

I referred this post: Calculate probability in normal distribution given mean, std in Python,

Also the scipy docs: scipy.stats.norm

But when I plot a PDF of a curve, the probability exceeds 1! Refer to this minimum working example:

import numpy as np
import scipy.stats as stats

x = np.linspace(0.3, 1.75, 1000)
plt.plot(x, stats.norm.pdf(x, 1.075, 0.2))
plt.show()

This is what I get:

How is it even possible to have 200% probability to get the mean, 1.075? Am I misinterpreting anything here? Is there any way to correct this?

解决方案

It's not a bug. It's not an incorrect result either. Probability density function's value at some specific point does not give you probability; it is a measure of how dense the distribution is around that value. For continuous random variables, the probability at a given point is equal to zero. Instead of p(X = x), we calculate probabilities between 2 points p(x1 < X < x2) and it is equal to the area below that probability density function. Probability density function's value can very well be above 1. It can even approach to infinity.

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