Tagged Questions
1
vote
1answer
65 views
Lower bounds of laplace transform of characteristic functions
I have the following integral:
\begin{equation}
f(\mu) = \int_0^\infty e^{-\mu t}\varphi_X(t)dt
\end{equation}
where $\varphi_X(t)$ is the characteristic function of some undetermined probability ...
1
vote
1answer
43 views
What is the distribution of empirical covariance between two independent normal distributions?
Suppose that we have two independent normal distributions $\mathcal{N}_{1}(0,s)$, $\mathcal{N}_{2}(0,t)$ what is the distribution of empirical covariance (or empirical correlation if this make my ...
1
vote
1answer
127 views
convolution square root of uniform distribution
I need to find a probability distribution function $f(x)$ such that the convolution $f * f$ is the uniform distribution (between $x=0$ and $x=1$). I would like to generate pairs of numbers with ...
0
votes
1answer
82 views
what's the distribution of the inverse of a random variable that follows a negative binomial distribution?
I was studying the method of moments estimation of parameters, and I encountered the following problem.
I have a geometric distribution as following:
$P(X=k) = p(1-p)^{k-1}$, and a sample size of n, ...
3
votes
3answers
206 views
Repeated convolution of probability distributions
Question
Let $$S_k=\sum_{i=1}^k X_i$$ be the sum of $k$ independent random variables. I am interested in closed-form expressions of the pdf of $S_k$.
In general, the pdf is given by the $k$-fold ...
2
votes
1answer
47 views
Fourier transform of product
I would like to know the fourier transform of the product of the Cauchy probability distribution $f(x)=\frac{1}{\pi (1+x^2)}, -\infty<x<\infty$ with itself.
I know that the fourier transform of ...
0
votes
1answer
70 views
Probability density of vector sum
Consider two unit $\mathbb R^2$ vectors $v$ and $w$. Then $v+w$ lies within a (closed) circle with radius 2, that is, in the region $x^2+y^2\leq4$.
Intuitively, the probability of $v+w$ lying close ...
0
votes
0answers
27 views
Distribution function approximation: Poisson exponentiation
I want to find normal approximation of Poisson exponentiation distribution.
Okay, some introduction to problem:
Assume that $\xi_i \sim F_{\lambda_i}(x)$ - Poisson distribution' random variables ...
1
vote
0answers
73 views
Poisson exponentiation distribution family and convolution
Assume $\xi_i \sim \mathbb{F}_{\lambda_i}(x)$ are random variables from Poisson distribution.
Consider random variables $\eta_i \sim \tilde{F}_{\lambda_i,t}(x)$, where $\tilde{F}_{\lambda_i,t}(x) = ...
0
votes
0answers
56 views
Weighted convolution?
Suppose I have two arbitrary discrete probability distributions with the same domain.
I want to convolve the two together to come up with third distribution, however I want them to be weighted.
...
3
votes
1answer
118 views
Estimating number drawn from one distribution based on sum of that number and number drawn from another distribution
I have been working on this for several days and have been unable to come up with an answer. The problem is very simple to state, but it seems difficult to solve.
A computer draws a number $x$ at ...
