Recent content by ecneicScience

Thanks for the tip.

That article didn't seem that helpful or it went way over my head. What I had in mind when you said a pdf could be reconstructed from its moments, is that the pdf could be approximated as some polynomial, where each term is somehow a function of the first N moments, and that the reconstruction...

Is there a theorem you could refer me to that describes this process of constructing a pdf from its moments?

Exactly! I never actually thought I'd use those convolution theorems I learned in my FT class! We know $$ h = f*g $$ Taking the Fourier transform $$ \mathcal{F}\{f*g\} = \mathcal{F}\{f\} \cdot \mathcal{F}\{g\} $$ We know f = g, so $$ \mathcal{F}\{f*g\} = \mathcal{F}\{f\}^2 $$ Rearranging, $$ f...

A common problem in statistics is, "Given that X is distributed according to the pdf f(x) and Y is distributed according to the pdf g(y), what is the pdf h(z) of Z = X + Y?" The answer is the convolution of f(x) and g(y): $$ h(z)=(f*g)(z)=\int_{-\infty}^\infty f(z-t)g(t) dt =...

Thank you very much for your insight. You made the arbitrariness of G(x) very clear to me. Sorry it took so long to get back to you.

My question is: suppose you have a function ##F(x)## which has an asymptote at ##x=x*##. Can you decompose ##F(x)## so that $$F(x) = G(x) + H(x)$$ where ##G(x)## is defined at ##x=x*## and ##H(x)## contains the asymptotic behaviour at ##x=x*## and goes to ##0## at plus or minus ##\inf##? This is...

Hello, My interests lie within the field of modelling biomolecular structure, function, and dynamics with computational and theoretical approaches. Is anyone aware of either top MSc or PhD programs offered by specific schools that are in line with this research direction? Thanks so much.