Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

The title says it all! When using orthogonal series expansions like the Gram-Charlier expansion to approximate probability density function, a big problem (making this approach less usefull and less mused than it could have been otherwise), is that, the approximation might be negative in some intervals, while a probability density function cannot be negative.

A quick thought assures us that two positive functions cannot be orthogonal, at lest not for the usual inner products of type $\int f(x) g(x) w(x) d\;x$.

So a natural idea is to ask for (non-orthogonal) expansions where each term in the expansion is non-negative. Does anybody know of any work in this direction?

share|improve this question
add comment

1 Answer 1

Aren't positive functions with non-overlapping support orthogonal?

share|improve this answer
    
I don't think they can appear as eigenfunctions of the underlying Sturm-Liouville problem, because said functions have a finite amount of zeros. –  Olivier Bégassat May 6 '11 at 3:07
    
Who said anything about an underlying Sturm-Liouville problem? –  Robert Israel May 20 '11 at 1:46
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.