All Questions
Tagged with fourier-transform characteristic-function
8 questions
3
votes
1
answer
95
views
Characteristic function of transformed random variable
Consider a random variable $X$ and a function $g(\cdot)$. Let $Y:=g(X)$, and let $\phi_X(\cdot), \phi_Y(\cdot)$ be the characteristic function (cf) of $X,Y$, respectively. Suppose that $\phi_X$ is non-...
- 583
3
votes
1
answer
94
views
Name of PDF? - projecting uniform probability distribution on the unit circle to the x-axis
Consider a uniform probability distribution on a circle of radius r, i.e. $\{(x,y) \in \mathbb{R}^2: x^2 + y^2 = r^2 \}$.If we wish to project onto the x-axis, we can consider each point on the circle ...
- 225
3
votes
1
answer
3k
views
Characteristic function and Fourier transform for a discrete random variable!
Let $\phi_{x}(t)= E [ e^{itx}]$ be the characteristic function
If X is a continuous random variable, then:
$\phi_{x}(t)= E [ e^{itx}] = \int e^{itx} f(x)dx$ (being $f(x)$ the probability density ...
- 31
6
votes
2
answers
1k
views
Sampling from characteristic/moment generating function
Suppose I am given a probability distribution only via its characteristic or moment generating function and I want to sample from that distribution to generate paths in a Monte Carlo simulation. Is ...
- 528
3
votes
1
answer
492
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How to compute bernoulli distribution PDF from CF
The characteristic function for a Bernoulli distribution is
$$\phi(t) = (q+pe^{it}) \text{ where } p+q=1$$
I also know that the relationship between $\phi(t)$ and the pdf $f(k)$ is the Fourier ...
- 33
1
vote
1
answer
582
views
Plot the density function of a normal random variable knowing only the characteristic function in R
The characteristic function of a normal random variable with mean $\mu$ and
standard deviation $\sigma$ is:
$$\begin{alignat*}{1}
\hat{\phi}(t) & =e^{i\mu t}e^{-\frac{1}{2}\sigma^{2}t^{2}}\\
&...
- 301
15
votes
1
answer
9k
views
Characteristic function and Fourier transform
I understand the definition of characteristic functions used in
probability theory:
For a random Variable $X$ with probability density function $f_X$ the characteristic function is defined as:
$$\...
- 1,401
3
votes
1
answer
706
views
Deconvolution with fourier transform or characteristic function?
Let us consider the following model:
$$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$
Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
- 1,401