Estoy tratando de entender el vínculo entre la función generadora de momento y la función característica. La función de generación de momento se define como:
Using the series expansion of , I can find all the moments of the distribution for the random variable X.
The characteristic function is defined as:
I don't fully understand what information the imaginary number gives me more. I see that and thus we don't have only in the characteristic function, but why do we need to subtract moments in the characteristic function? What's the mathematical idea?