i) The cumulant function is the Laplace transform of the probability distribution. Uniqueness of Laplace transforms then tells you that the cumulant function can be used to fully characterize …

But cumulant sequences have a nice property that moment sequences don't have: the set of all such sequences is closed under addition. So draw a ray out from the origin $(0,0,0,\ldots)$. If …

2024年1月17日 · The cumulant expansion polynomials, as discussed in A263634, are intimately linked to the Appell Sheffer finite op calc / umbral calculus as well. As noted in A127671, they …

2021年8月2日 · $\begingroup$ I see: Given your way of (incorrectly) using the word "derive", I now suspect you meant to ask how the 4th-order cumulant is defined. $\endgroup$ – Michael …

2023年10月6日 · $\begingroup$ There are some papers of Soshnikov which are in this direction, though they don't answer your question as it seems like it would take some real book-keeping …

2020年3月12日 · The cumulant is the log of the Fourier transform of a specific function. But the paper you link, and my comment, are about taking the log of the Fourier transform operator in …

2015年3月24日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

2022年1月4日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

2021年6月24日 · For example, in these slides, it is claimed both moments generating functions and cumulant generating functions have the same radius of convergence. pr.probability …

2017年1月11日 · If you translate the bound on moment generating function $\mathbf E e^{i t X}$ onto $\log\mathbf E e^{itX}$ using the relation between moments and cumulants (see, Mobius …