Conditional cumulants form a set of unique statistics which represent a sensible compromise between N -point correlation functions and cumulants measured from moments of counts in cells. They share accurate edge corrected estimators with N -point correlation functions, yet, they are as straightforward to measure and interpret as counts in cells. The conditional cumulants have three equivalent v...

We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed.

This paper deals with power-quality (PQ) event detection, classification and characterization using higher-order sliding cumulants to examine the signals. Their maxima and minima are the main features, and the classification strategy is based in competitive layers. Concretely, we concentrate on the task of differentiating two types of transients (short duration and long duration). By measuring ...

An interpretation for the use of cumulants in narrowband array processing problems is proposed. It is shown how fourth-order cumulants of multichannel observations increase the directional information compared with second-order statistics. Based on the interpretation, it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array. The amount of partial in...

Compared with bispectrum, three-order cumulants have a lower computing complexity, and complex threeorder cumulants formally includes different coupling information of signals, in the experiment, through these different coupling modes, features of fault signals and normal signals are fetched by 2-D wavelet in different directions, then these features are used to diagnose fault. The experiment s...

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for 'moments' of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including ...

Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and rstorder transitions in the phase diagram of a well known spin-1 Ising model. Simple ideas from the theory of thermodynamic uctuations...

The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants t...

Cognitive radios (CRs) require efficient spectrum detectors that are able to work in low signal-to-noise ratio (SNR) environments. These detectors have little or no information about the signals or noise to utilize the spectrum in an efficient manner. The present paper proposes an autonomous policy-based CR focusing on policy management using spectrum sensing. A separate wireless communication ...

We have calculated the large-q expansion for the energy cumulants at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in 1/ √ q using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for q > 4 on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya e...