A Simple and Pragmatic Approximation to the Normal Cumulative Probability Distribution
A Simple and Pragmatic Approximation to the Normal Cumulative Probability Distribution
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正态累积概率分布的简单实用的近似
DOI：
10.2139/ssrn.2579686
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Bell
中科院分区：
文献类型：
--
作者：
J. Bell
随机变量和统计是计量经济学的核心。概率分布将概率分配给随机变量。累积概率描述了随机变量不会超过给定值的概率。正态概率分布（也称为高斯分布）是计量经济学、统计学和工程学中最常用的分布。正态分布随机变量的累积概率不能用初等函数表示，必须在表格中找到，从计算机程序中找到，或者近似。本文提供了一个简单而实用的分析近似的累积概率的正态分布的随机变量，便于背面的信封计算。这种近似的最大绝对误差约为0.003。该精度足以满足大多数实际应用。它还提供了给定概率下随机变量上限值的简单逆计算。
Random variables and statistics are at the very center of Econometrics. Probability distributions assign a probability to a random variable. The cumulative probability describes the probability that a random variable will not exceed a given value. The normal probability distribution (also known as the Gaussian distribution) is the most commonly used distribution in econometrics, statistics, and engineering. The cumulative probability of a normally distributed random variable cannot be expressed in terms of elementary functions and must be found in tables, from computer programs, or be approximated. This paper offers a simple and pragmatic analytical approximation to the cumulative probability of a normally distributed random variable for easy back-of-the-envelope calculations. This approximation has a maximum absolute error of about 0.003. This accuracy is sufficient for most practical applications. It also provides for easy inverse calculations of the upper value of a random variable for a given probability.