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

Quote:

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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

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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.

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.