Probabilities from pdf does not sum to 1

Hello,

I have fitted a distribution function to some empirical data... I applied Weibull, Fréchet and Gumbel distribution fitting.

When I compute the expected probabilities of my Weibull P(x=1), P(x=2), P(x=3), P(x=4) and P(x=5) (my dataset is defined from 1 to 5...) The sum of the probabilities is 1.0012, even if i ask matlab to compute the sum (there should be no problems due to wrong rounding).

I do not have such a problem with the two other distributions that either sums up to 1.000 or to a value smaller than 1.

I do not understand where the problem for Weibull comes from. Moreover, when I compute the cdf of the Weibull and ask P(x<=5) I get 1.0000 as answer.

If anyone has an idea or an explication, thank you very much!

AuW

Answer 1

[Matt J]

These are pdfs, not pmfs. Their integrals should be 1, but nothing can be said about their sums over an arbitrary set of discrete points like 1,...,5.

[Aurélie]

Thank you a lot for your help!