What is Normal Distribution?
1430 reads · Last updated: December 5, 2024
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.In graphical form, the normal distribution appears as a "bell curve".
Definition
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, indicating that data near the mean are more frequent in occurrence than data far from the mean. When graphed, the normal distribution appears as a bell-shaped curve.
Origin
The concept of the normal distribution originated in the late 18th and early 19th centuries, developed by mathematician Carl Friedrich Gauss. Gauss introduced this concept while studying errors in astronomy. Over time, the normal distribution became a fundamental concept in statistics and probability theory.
Categories and Features
The main features of the normal distribution are its symmetry and bell-shaped curve. It is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the center of the distribution, while the standard deviation determines the width. The standard normal distribution is a special case where the mean is 0 and the standard deviation is 1. The normal distribution is widely used in natural and social sciences to describe many natural phenomena and measurement errors.
Case Studies
A typical case is the distribution of stock market returns. Although actual market returns do not perfectly follow a normal distribution, assuming returns are normally distributed can simplify the analysis process in many financial models. Another example is the distribution of measurement errors. In many experiments, measurement errors are assumed to be normally distributed because this assumption can be supported by the central limit theorem.
Common Issues
Investors may encounter issues when applying the normal distribution, such as mistakenly assuming that all financial data follow a normal distribution. In reality, many financial data may have fat tails or skewness, meaning their distribution may deviate from normality. Additionally, over-reliance on the normal distribution assumption can lead to underestimating risk.
