# Tagged Questions

**6**

votes

**4**answers

432 views

### Laplace transform on the cone of positive-definite matrices

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 in $P_p$ by (for ...

**1**

vote

**2**answers

1k views

### Inversion of Moment-generating functions (aka Laplace transform of prob dist)

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{equation}
Since I have ...

**0**

votes

**1**answer

125 views

### How are epidemic models simulated in case of mobility?

I am not a mathematician but out of curiosity I am trying to implement the SIS epidemic model when the nodes have mobility to understand how it will change the results. I understand how to perform ...

**0**

votes

**1**answer

8k views

### Difference between Principal Component Analysis(PCA) and Singular Value Decomposition(SVD)?

I am confused between PCA and SVD.
The wikipedia page for PCA has this line. "PCA can be done by eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, ...

**7**

votes

**4**answers

1k views

### Estimating the probability that one Poisson RV is larger than another

Let $X$ and $Y$ be Poisson random variables with means $\lambda$ and $1$, respectively. The difference of $X$ and $Y$ is a Skellam random variable, with probability density function
$$\mathbb P(X - Y ...

**1**

vote

**1**answer

326 views

### Statistical inequality

Let $X$ be a finite discrete variable and $X\ge0$. Is it true that
$$16\operatorname{Var}(X) \le \left[8{\mathbb E}(X) + \operatorname{Range}(X)\right]\operatorname{Range}(X)$$
where ...

**17**

votes

**1**answer

1k views

### Intuitive Proof of Cramer's Decomposition Theorem

Cramer's decomposition theorem states that if $X$ and $Y$ are independent real random variables and $X+Y$ has normal distribution, then both $X$ and $Y$ are normally distributed. I've seen a few ...

**2**

votes

**7**answers

596 views

### Splines, harmonic analysis, singular integrals.

Apologies if my question is poorly phrased. I'm a computer scientist trying to teach myself about generalized functions. (Simple explanations are preferred. -- Thanks.)
One of the references I'm ...

**2**

votes

**5**answers

588 views

### Statistical Data Analysis

For personal research, I'm doing some analysis on collected data and trying to develop relationships between two variables where the data is collected through a data logger. I'm hypothesising that a ...

**1**

vote

**2**answers

1k views

### Multiple outliers for two variable linear regression

Problem
Visually, the "extreme" outliers in the following graph are somewhat obvious:
http://i.imgur.com/tiSbS.png
Question
Given:
T - Set of all temperatures
Y - Set of all years
ΣT - Sum of ...

**7**

votes

**4**answers

699 views

### What m minimizes E(|m-X|^3) for a random variable X?

Let X be a random variable. Then E(|m-X|^1) is minimized when (as a function of m) when m is the median of X, and E(|m-X|^2) is minimized when m is the mean of x.
A couple weeks ago in a technical ...