Glossary
Probability Density Function (PDF)
A function that describes the relative likelihood for a continuous random variable to take a given value. The probability of the variable falling within a particular interval is the integral of the density over that interval. The total area under the density curve equals one.
Definition
A function that describes the relative likelihood for a continuous random variable to take a given value. The probability of the variable falling within a particular interval is the integral of the density over that interval. The total area under the density curve equals one.
Why It Matters
The PDF is the continuous analogue of a probability mass function and is fundamental to statistical modelling. Every parametric model — from the Normal distribution to GARCH volatility models — is defined by its density function. Understanding PDFs is essential for interpreting likelihood functions, computing probabilities, and selecting appropriate distributions for data.
Example
The Normal distribution's PDF, the familiar bell curve, shows that values near the mean are most probable while extreme values are increasingly unlikely. The area under the curve between two points gives the probability of observing a value in that range — for instance, roughly 68% of values fall within one standard deviation of the mean.
Related Terms
Software Notes
- SPSS: Transform > Compute Variable; use
PDF.Normal,PDF.Standard, etc. - R:
dnorm(),dpois(),dbinom()and otherd*functions for specific distributions - Stata:
normalden()for the Normal PDF;display normalden(0)returns the density at zero