Intro to Random Vibration Peak Distribution

November 7, 2023

This section of the “Ask Joel” videos explains random vibration peak distribution, specifically, the probability density function (PDF) of random data.

Probability Density Function & Gaussian Distribution

Due to the nature of random vibration, the time-domain data of multiple test runs will contain different peak accelerations for any given time. The probability density function (PDF) is a tool that allows test engineers to approximate the peak vibration levels of a random signal. The PDF is a histogram of a signal’s probable peak distribution, providing the likelihood of a particular vibration level.

Random vibration testing assumes a Gaussian distribution of data, which four key statistical concepts (mean, variance, skewness, and kurtosis) can help to explain.


Kurtosis is a statistical measurement that describes the distribution of data about the mean value. Kurtosis defines the “tails” of the PDF, meaning how the data’s peak values stray from the mean. Data with higher kurtosis values have longer PDF “tails,” meaning they contain a greater quantity of high peak values.

Increasing the kurtosis of a random vibration test redistributes the data to have higher peak accelerations while maintaining the same test energy.

Increasing the kurtosis of a random vibration test decreases the time needed to bring a product to failure. Engineers may also evaluate the kurtosis of a test to make it more realistic. Research has shown that real-world data is not always Gaussian.

Learn more: Probability Distribution of Random Vibration