Let $X_1$, $X_2$, ..., $X_n$ be iid RV's with range $[0,1]$ but unknown distribution. (I'm OK with assuming that the distribution is continuous, etc., if necessary.) Define $S_n …

In Stigler's (1977) ``Fractional order statistics, with applications,'' he says (page 545) that he considers a special case of Ferguson's (1973) Dirichlet process (DP). Specifical …

Hello everyone, I have a problem and I really don't know what kind of mathematical method should I apply to solve or model my problem. I would be thankful If anyone can give me so …

Suppose I have two variables $X$ and $Y$ which have continuous p.d.f.s $f$ and $g$ on the positive real line. I know that the moments $\mathrm{E}[X^n] > \mathrm{E}[Y^n]$ for suffic …

I have a two-index succession of real-valued random variables $x_{t,n}$ such that $\lim_{n\to\infty} x_{t,n} = x_t$, for all $t$ and suitable limit r.v. $x_t$. I would like to pro …

A sort of continuation of http://mathoverflow.net/questions/96165/comparing-distributions-with-moments Suppose I have some estimates of the moments of a non-negative random variab …

Let $S$ be a vector of length $n$ where each entry follows a Normal distribution. We know that one entry (say, at some index $s$ which we don't know) follows $\mathcal{N}(E_c,V_c/m …

This question deals with 2D random walks on continuous space (not lattices). A continuous-time persistent random walk is one where the particle 'remembers' its velocity $v(t)$ for …

The title says most. Let $P_p$ be the cone of positive-definite $p \times p$ matrices. One can define the Laplace transform of (the distribution of) a random matrix with values i …

This is a generalization of a previous MO question, "Reducing system of equations involving Erf, Error Function". Consider the system of equations: $$1/2 + {\rm Erf}(x) - \alpha …

I have a system of equations: $$1/2 + {\rm Erf}(x) - {\rm Erf}(\frac{x+y}{2})=0$$ $$-1/2 + {\rm Erf}(y) - {\rm Erf}(\frac{x+y}{2})=0,$$ Where $x \le y$ and ${\rm Erf}$ is the Err …

I'm not quite sure about how to define a good measure of the quality of a communication channel with fading and interference. Let us assume the simplest case, where a node in a net …

The Problem of the Mad King's Draft: Suppose there is country which is ruled by a king who can be either 'mad' or 'normal.' The king rules a a large country with a continuum of ci …

Suppose I am dead-set on using Bayesian inference on independent and identically distributed data, but I'm lazy and insist on using a parametric likelihood function come what may. …

I want to embark on a project about inverting a Moment-generating function of a probabilitiy distribution. That is given by \begin{equation} M_X(t) = \text{E} \exp(tX) \end{eq …