What information does a probability density function (PDF) graph provide?

This sounds like a simple question and I know PDF graphs are used a lot in presentations and financial publications. Yet, what information does it actually provide? The CDF actually gives you probabilities of the random variable falling within a certain range. The PDF does not tell you the probability of a particular random variable of occurring (that is 0). It also doesn't tell you the probability of a range of random variables occurring (you'll need to do an integral for that). I can't think of any information a PDF would tell you that a CDF can't, yet I rarely/almost never see CDFs in presentations or financial publications.

What am I missing here? What information should I discern when I look at a PDF?

• It's much easier to quickly see in the PDF than in the CDF what areas of the support/domain have more or less probability mass Jul 25, 2019 at 14:28
• The visual analog of "do an integral" is "estimate the area." But that's not entirely what the PDF is for: it helps you see a rate of change (of the CDF) by means of the heights of graphical symbols: that's one of the best and most reliable ways to represent quantitative information visually and can be extremely difficult to extract from a graph of the CDF itself.
– whuber
Jul 25, 2019 at 19:38

You're right that the PDF and CDF give the same information. They better! The CDF is the integral of the PDF.

Explicitly visualizing the PDF can be helpful, however. Looking at PDFs allows for judgments about location, scale, skewness, multimodality, etc, that aren't necessarily as easy to see from a CDF, particularly when you aren't used to inferring such information from a CDF, but we've all been looking at histograms since we were in high school, right? (I'm taking a histogram as an approximation of the PDF.)

Edit: I love Jake's comment to the original question. "It's much easier to quickly see in the PDF than in the CDF what areas of the support/domain have more or less probability mass" which is the gist of this answer.

• Well I'm saying the graph of a CDF provides more information than the PDF. So I was wondering why graphs of PDFs are more prevalent and why do I rarely see graphs of CDFs unless I'm reading a stats text. The popularity of PDF graphs must imply that they convey some information that I didn't realize they convey, otherwise, why aren't CDFs more widely used. But multimodality is a good/useful one that I would imagine that CDFs won't be able to convey. Jul 25, 2019 at 14:23
• Yes multimodality is a good one that CDFs won't easily convey but histograms are not the same thing as PDFs as the interpretation is different. Which furthers my dislike of PDFs as it took me awhile to realize that the y-axis of a PDF does not tell me the quantity nor probability of a variable occurring. The y-axis of a PDF doesn't tell you anything. For a CDF, both the y-axis and x-axis convey information. Jul 25, 2019 at 14:28
• The y-axis of a PDF conveys the likelihood!
– Dave
Jul 25, 2019 at 14:38
• What do you mean? For a standard normal distribution, the y-axis ranges from 0 to about 0.4. When x is 0 and y is 0.4, that doesn't tell me anything like the typical histogram. The 0.4 doesn't mean anything unless I'm understanding stuff wrong. Jul 25, 2019 at 14:46
• @confused I think Dave means likelihood in the technical sense, as in likelihood function Jul 25, 2019 at 15:05