PDF-->CDF

[MoeSzyslak]

Hi, All --

So I have a PDF represented by discrete data points. I have splined this and integrated it, so I should get the CDF, right? Instead, the results look a little funky. What am I missing?

Matt

[Werner_E · Accepted solution]

Instead, the results look a little funky.

Why? What result did you expect? It looks OK to me. If you expected a slower approach to 1 - look at the graph without the log scale at the abscissa.

[MoeSzyslak]

If I look at, say x = 1, it looks like I should have more than ~20% of the area under the PDF accumulated, but maybe it's just the log scale playing tricks on my intuition?

[Werner_E]

but maybe it's just the log scale playing tricks on my intuition?

I think that is it - turn off log scale just for a moment and have a look. Lower values of x are very largely stretched by the log scale and this gives the impression of a bigger area under the curve than it is. You have a high, but only very narrow spike at x=0.5. Without log scale it looks more reasonable that we have 50% around x=5.3 - it looks impossible with log scale, though.

[AlanStevens]

Moe Szyslak wrote:

...but maybe it's just the log scale playing tricks on my intuition?

I think so too. You get much the same curve by doing a simpler calculation of the area using the mean value of adjacent points:

Alan