Think Stats, 2nd Edition

Chapter 6. Probability Density Functions

The code for this chapter is in density.py. For information about downloading and working with this code, see Using the Code.

PDFs

The derivative of a CDF is called a probability density function, or PDF. For example, the PDF of an exponential distribution is

The PDF of a normal distribution is

Evaluating a PDF for a particular value of x is usually not useful. The result is not a probability; it is a probability density.

In physics, density is mass per unit of volume; in order to get a mass, you have to multiply by volume or, if the density is not constant, you have to integrate over volume.

Similarly, probability density measures probability per unit of x. In order to get a probability mass, you have to integrate over x.

thinkstats2 provides a class called Pdf that represents a probability density function. Every Pdf object provides the following methods:

• Density, which takes a value, x, and returns the density of the distribution at x.

• Render, which evaluates the density at a discrete set of values and returns a pair of sequences: the sorted values, xs, and their probability densities, ds.

• MakePmf, which evaluates Density at a discrete set of values and returns a normalized Pmf that approximates the Pdf.

• GetLinspace, which returns the default set of ...