Questions tagged [characteristic-functions]

Questions about characteristic functions, of a set (which gives $1$ if the element is on the set and $0$ otherwise) or of a random variable (its Fourier transform). Do not use this tag if you are asking about the method of characteristics in PDE or the characteristic polynomial in linear algebra.

1,096 questions
Filter by
Sorted by
Tagged with
29 views

22 views

38 views

How to find or approximate probability distribution from known values of the characteristic function?

If I have a known discrete values for the characteristic function (I know $a_n$ values for specific values of $\omega_n = \frac{2\pi i n}{d}$): $$a_n = \phi_x\left(\omega = \frac{2\pi in}{d}\right),$$ ...
36 views

Questions about point (xi) of consistency checks from Eigenvlaue - Eigenvector Identity by Terence Tao.

In the recent paper by Tao concerning the famous eigenvalue-eigenvector identity, I need some help in understand the (xi) point under basic consistency checks. The actual identity (2) given in the ...
33 views

45 views

Given a r.v. $X$, can we choose a r.v. $Y$ independent of $X$ and with the same distribution?

The question originates in the following problem: Given that $\phi$ is a characteristic function, show that so is $| \phi |^2$. The solution given by a lecturer was as follows: Suppose $\phi$ is the ...
56 views

Lévy-Khintchine canonical representaion of Gamma distribution

what is the Lévy-Khintchine representation of an infinitely divisible characteristic function(ch.f.). such as Gamma distribution (ch.f. $$f(x)=(1-\frac{ix}{\lambda})^r$$) I wonder if there is any good ...
44 views

Curve problem $x = x_0 + te^{x_0+1}.$
I'm studying characteristic curves in PDE. In one of the problems I was doing, I came up with the following characteristic equation: $$x = x_0 + te^{x_0+1}.$$ I need to isolate $x_0$ to proceed with ...