为什么scipy.norm.pdf有时会给PDF> 1个如何纠正？

问题描述

给出高斯（正常）随机变量的均值和方差，我想计算其概率密度函数（PDF）。

我提到了这篇文章：

如何甚至有200％的概率获得均值，1.075？我在这里误解什么吗？

解决方案

这不是错误。这也不是不正确的结果。概率密度函数在某些特定点的值不会给您带来概率；它衡量分布如何围绕该值进行密集。对于连续随机变量，给定点处的概率等于零。代替 p（X = x），我们计算两个点之间的概率 p（x1< X< x2），它等于该概率密度函数下方的面积。概率密度函数的值可以很好地大于1。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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