# Thread: Probability Density Function Sums to 1?

1. ## Probability Density Function Sums to 1?

Hi,
I was looking at the probability density functions (PDF) on Wikipedia for various distributions, such as Uniform, Normal, Pareto, Exponential, and Weibull.

The first two of those distributions have a PDF who integral is one, however the last 3 have PDFs which do not seem to integrate to one. I quickly observed this by quickly looking at the graph of the PDF.

I thought that the area under a PDF must always sum to one. So what has gone wrong here? I was going to query this on the talk pages on Wikipedia , but I figured I would ask here first in case I'm misunderstanding something to do with PDFs.

thanks
Andrew

2. Originally Posted by bramp
Hi,
I was looking at the probability density functions (PDF) on Wikipedia for various distributions, such as Uniform, Normal, Pareto, Exponential, and Weibull.

The first two of those distributions have a PDF who integral is one, however the last 3 have PDFs which do not seem to integrate to one. I quickly observed this by quickly looking at the graph of the PDF.

I thought that the area under a PDF must always sum to one. So what has gone wrong here? I was going to query this on the talk pages on Wikipedia , but I figured I would ask here first in case I'm misunderstanding something to do with PDFs.

thanks
Andrew
The area under the pdf curve is equal to 1. Show the details of your attempt to calculate this area for Pareto, Exponential, and Weibull pdf's.

3. I might not have made it clear, but I quickly inferred that the area under the graph can't sum to one. I didn't try and integrate this myself. Take for example the Pareto's PDF graph: Image:Pareto distributionPDF.png - Wikipedia, the free encyclopedia

Surely since there are values greater than 1, then the area can't sum to one.

BUT OOOOH. I think I've just understood where my problem is!

The PDF may be greater than one, but if, for example, it is only above one between 0>=x>=0.5, then the integral won't necessary be greater than one.

anyway, sorry I think I just made a rookie mistake, and miss a fundamental thing. Problem solved.