# Questions tagged [moments]

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### Harmonic mean or generating function, pick one?

Is there an obvious or a profound reason for the dearth of statistical distributions for which analytical harmonic mean and moment generating functions co-exist? Are there good examples (with finite ...
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### A Minkowski-like inequality

Assume that $X$ and $Y$ are two arbitrary non-negative random variables. Is the following inequality true for $1\leq\alpha\leq 2$? \begin{align} \left(\mathbb{E}\left[X^\alpha\right]-\mathbb{E}\left[...
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### Fourth moments of Gaussian processes

I am working on a topic outside my main research area, so I am afraid I am reproving obvious results, so I would like to ask for a reference. Google didn't help, mostly because I am looking for ...
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### Moment problem on [-1,1]: necessary and sufficient conditions

Consider a sequence of real numbers $s=(s_0,s_1,\ldots)$. When is there a Borel measure $\mu$ supported on $[-1,1]$ so that $$s_k = \int_{[-1,1]} x^k\,\mathrm{d}\mu,\quad \forall k\in\mathbb N\;?$$ ...
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### Computing skewness derivative in terms of variance

In the Portilla Simoncelli paper (page 18): http://www.cns.nyu.edu/pub/lcv/portilla99-reprint.pdf They go about calculating the derivative of the skewness $\eta(x)$ of a distribution (2D matrix in ...
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### Gaussian and the convex hull of moment curves

Let $c_1,\dots, c_d$ be the first $d$ moments of the standard normal distribution. Does the point $(c_1,\dots, c_d)$ lie in the convex hull of the set $\{(t,t^2,\dots,t^d)\colon t\in[-b,b]\}$, for a ...
This is a question related to the statistical model behind independent component analysis (ICA). We assume that $Z \sim N(0,1)$. Our goal is to construct a random variable $X$ that follows a ...
Let $D$ be a bounded simply connected domain in the plane, bounded by a smooth closed curve $\partial D$. Moreover$D$ contains the origin. Assume that all negative complex moments w.r.t arc-length ...