Normal Distribution Generator
Generate normally distributed (Gaussian) random numbers using Box-Muller algorithm with customizable mean and standard deviation, histogram visualization and data export
Parameter Settings
Documentation
What is Normal Distribution?
Normal Distribution, also known as Gaussian distribution, is one of the most important probability distributions in statistics. It features a bell-shaped curve centered around the mean, with approximately 68% of data falling within one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations. It is widely used in natural sciences, social sciences, and engineering.
Box-Muller Algorithm
This tool uses the Box-Muller transform algorithm to generate normally distributed random numbers. The algorithm converts two independent uniformly distributed random numbers into two independent standard normal random numbers using polar coordinate transformation, providing both efficiency and accuracy.
Visualization
The tool provides histogram visualization, grouping generated data into intervals for statistical display, allowing you to intuitively observe the data distribution and verify whether it conforms to normal distribution characteristics.
Use Cases
Scientific Research
Experimental data simulation
Machine Learning
Weight initialization
Financial Analysis
Risk model building
Quality Control
Measurement error analysis
How to Use
- Set the mean (M) and standard deviation (SD) parameters to determine the center and dispersion of the distribution
- Set the count (N), decimal places, and separator type
- Click the "Generate" button to view results, statistics, and distribution histogram. You can export or copy the data
Notes
- • Standard deviation must be greater than 0, otherwise valid normal distribution data cannot be generated
- • Count is limited to 1-10000. The larger the count, the closer the distribution approaches theoretical normal distribution
- • Generated numbers are pseudo-random, suitable for simulation and testing, not recommended for cryptographic or security applications
FAQ
What do mean and standard deviation control?
The mean (M) determines the center of the distribution, while the standard deviation (SD) determines the degree of data dispersion. A larger standard deviation means more scattered data; a smaller standard deviation means data is more concentrated around the mean.
Why are the generated statistics different from the set values?
Due to randomness, finite sample statistics will have some deviation from theoretical values. This is normal. The larger the sample size, the closer the statistics will be to the theoretical set values.
Are the generated numbers truly random?
They are pseudo-random numbers based on JavaScript's Math.random() function and the Box-Muller transform algorithm. They are sufficient for most simulation and testing scenarios but are not suitable for cryptographic applications requiring true randomness.
How to verify if data follows normal distribution?
You can observe whether the histogram shows a bell-shaped curve, or check if the actual mean and standard deviation in the statistics are close to the set values. The larger the sample size, the closer the distribution approximates the ideal normal distribution.