Tagged Questions
1
vote
0answers
33 views
Is it possible to calculate mutual information by moments generating functions?
I went to listen to a workshop and some audience asked the presenter how the moments can improve the mutual information. I am learning the MI(Mutual Information) and moments so don't have enough ...
1
vote
1answer
102 views
Proving that MGF determines PDF when the PDF is defined for whole real line
If two PDFs have the same moment generating function that converges in an open set around 0, then the PDFs are same.
This is a well known fact, but I can't find its proof. If the PDFs are defined ...
4
votes
1answer
390 views
Link between moment-generating function and characteristic function
I am trying to understand the link between the moment-generating function and characteristic function. The moment-generating function is defined as:
$$
M_X(t) = E(\exp(tX)) = 1 + \frac{t E(X)}{1} + ...
1
vote
1answer
526 views
How can I calculate central moments of a joint pdf?
Let's say I have two signals $x_1$ and $x_2$, each having $N$ samples, i.e.:
$$ x_1 = \{ x_{11}, x_{12}, ..., x_{1N} \} $$
$$ x_2 = \{ x_{21}, x_{22}, ..., x_{2N} \} $$
The signals are both ...
1
vote
2answers
456 views
If the n(th) moment exists does it mean all smaller moments exist too?
I would like to prove the following statement:
If the $r$th moment of a random variable $X$ exists and is finite,
then all moments $1$ to $r-1$ exist and are finite.
Edit: I mean the raw ...
0
votes
0answers
181 views
Moments of function of Poisson process
Mirror thread on Mathoverflow.
(I'm new to Poisson processes, so please edit if my terminology is incorrect.)
This is a special case of a problem I'm working on; hoping for intuition that will ...
9
votes
3answers
151 views
Approximating $Pr[n \leq X \leq m]$ for a discrete distribution
What's the best way to approximate $Pr[n \leq X \leq m]$ for two given integers $m,n$ when you know the mean $\mu$, variance $\sigma^2$, skewness $\gamma_1$ and excess kurtosis $\gamma_2$ of a ...
