Measuring Dispersion and Serial Dependence in Ordinal Time Series Based on the Cumulative Paired ϕ-Entropy

The family of cumulative paired ϕ-entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s κ, with the weights being related to the actual choice of ϕ. Again, the asymptotic distribution of the corresponding sample κϕ is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel ϕ-entropy-related measures are applied to an ordinal time series on the daily level of air quality.

Global Warming Signals in Brazil and its Macro-Regions - Trend Analysis of Distributional Characteristics Characteristics

The aim of this research is to study global warming signals across Brazil. This investigation uses approximately 60 years of daily temperature data set and applies a recent trend test proposed by Rivas and Gonzalo (2020) which analyses not only the average but also different distributional characteristics. Besides, the test provides robust results for both I(0) and I(1) processes. We found significant trends in almost all characteristics in the analysis of the whole country. The mean and the maximum are increasing over time and the dispersion measures indicate decreasing trends. For the region analysis, we found out that, apart from the South, which does not appear to be drastically affected by global warming, the other regions present clear signs of global warming.

The First CHIME/FRB Fast Radio Burst Catalog

We present a catalog of 536 fast radio bursts (FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst (CHIME/FRB) Project between 400 and 800 MHz from 2018 July 25 to 2019 July 1, including 62 bursts from 18 previously reported repeating sources. The catalog represents the first large sample, including bursts from repeaters and nonrepeaters, observed in a single survey with uniform selection effects. This facilitates comparative and absolute studies of the FRB population. We show that repeaters and apparent nonrepeaters have sky locations and dispersion measures (DMs) that are consistent with being drawn from the same distribution. However, bursts from repeating sources differ from apparent nonrepeaters in intrinsic temporal width and spectral bandwidth. Through injection of simulated events into our detection pipeline, we perform an absolute calibration of selection effects to account for systematic biases. We find evidence for a population of FRBs—composing a large fraction of the overall population—with a scattering time at 600 MHz in excess of 10 ms, of which only a small fraction are observed by CHIME/FRB. We infer a power-law index for the cumulative fluence distribution of α = − 1.40 ± 0.11 ( stat. ) − 0.09 + 0.06 ( sys. ) , consistent with the −3/2 expectation for a nonevolving population in Euclidean space. We find that α is steeper for high-DM events and shallower for low-DM events, which is what would be expected when DM is correlated with distance. We infer a sky rate of [ 820 ± 60 ( stat. ) − 200 + 220 ( sys. ) ] / sky / day above a fluence of 5 Jy ms at 600 MHz, with a scattering time at 600 MHz under 10 ms and DM above 100 pc cm−3.

What do (most of) our dispersion measures measure (most)? Dispersion?

This paper discusses the degree to which most of the most widely-used measures of dispersion in corpus linguistics are not particularly valid in the sense of actually measuring dispersion rather than some amalgam of a lot of frequency and a little dispersion. The paper demonstrates these issues on the basis of data from a variety of corpora. I then outline how to design a dispersion measure that only measures dispersion and show that (i) it indeed measures information that is different from frequency in an intuitive way and (ii) has a higher degree of predictive power of lexical decision times from the MALD database than nearly all other measures in nearly all corpora tested.

Statistical Measurements of Dispersion Measure Fluctuations of FRBs

Extragalactic fast radio bursts (FRBs) have large dispersion measures (DMs) and are unique probes of intergalactic electron density fluctuations. By using the recently released First CHIME/FRB Catalog, we reexamined the structure function (SF) of DM fluctuations. It shows a large DM fluctuation similar to that previously reported in Xu & Zhang, but no clear correlation hinting toward large-scale turbulence is reproduced with this larger sample. To suppress the distortion effect from FRB distances and their host DMs, we focus on a subset of CHIME catalog with DM < 500 pc cm−3. A trend of nonconstant SF and nonzero correlation function (CF) at angular separations θ less than 10° is seen, but with large statistical uncertainties. The difference found between SF and that derived from CF at θ ≲ 10° can be ascribed to the large statistical uncertainties or the density inhomogeneities on scales on the order of 100 Mpc. The possible correlation of electron density fluctuations and inhomogeneities of density distribution should be tested when several thousands of FRBs are available.

What do (some of) our association measures measure (most)? Association?

This paper discusses the degree to which some of the most widely-used measures of association in corpus linguistics are not particularly valid in the sense of actually measuring association rather than some amalgam of a lot of frequency and a little association. The paper demonstrates these issues on the basis of hypothetical and actual corpus data and outlines implications of the findings. I then outline how to design an association measure that only measures association and show that its behavior supports the use of the log odds ratio as a true association-only measure but separately from frequency; in addition, this paper sets the stage for an analogous review of dispersion measures in corpus linguistics.

Volatility and Dispersion of Hourly Electricity Contracts on the German Continuous Intraday Market

Intraday electricity trading on the continuous intraday market of EPEX SPOT is particularly well suited for the rebalancing of energy production. We analyzed the volatility and dispersion of individual hourly contracts, taking into account the particularities of the market, due to which the standard volatility measure from financial time series cannot be applied. We used and analyzed five measures for price fluctuations, which turned out to be similarly well suited for electricity contracts, with small differences. We then identified fundamental drivers of price fluctuations: the relative share of wind in the overall mix increased dispersion. In addition, price dispersion was positively correlated with the traded volume as well as the absolute difference between the day-ahead auction price and the volume-weighted intraday price. We furthermore analyzed the timely structure of price fluctuations to identify forecast indicators for a contract’s peak trading hour before maturity, finding that trading-related variables are more important to forecast price fluctuations than fundamental factors. With lagged realizations and additional external drivers, forecast regressions reached an adjusted R2 of 0.479 for volatility and around 0.3 for the dispersion measures.

Algebraic Lq-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics

The Jacobi polynomials $\hat{P}_n^{(\alpha,\beta)}(x)$ conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight function $(1-x)^\alpha (1+x)^\beta, \alpha,\beta>-1,$ on the interval $[-1,+1]$. The spreading of its associated probability density (i.e., the Rakhmanov density) over the orthogonality support has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic $\mathfrak{L}_{q}$-norms (Shannon and R\’enyi entropies) and the monotonic complexity-like measures of Cram\’er-Rao, Fisher-Shannon and LMC (L\’opez-Ruiz, Mancini and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters $(\alpha,\beta)$ are large. In this work, we determine in a simple, compact form the leading term of the entropic and complexity-like properties of the Jacobi polynomials in the two extreme situations: ($n\rightarrow \infty$; fixed $\alpha,\beta$) and ($\alpha\rightarrow \infty$; fixed $n,\beta$). These two asymptotics are relevant \textit{per se} and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of many exactly, conditional exactly and quasi-exactly solvable quantum-mechanical potentials which model numerous atomic and molecular systems.

Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes

Variance, as a measurement of dispersion, is a basic component of decision-making processes. Recent advances in intelligent systems have included the concept of variance in information fusion techniques for decision-making under uncertainty. These dispersion measures broaden the spectrum of decision makers by extending the toolset for the analysis and modeling of problems. This paper introduces some variance logarithmic averaging operators, including the variance generalized ordered weighted averaging (Var-GOWLA) operator and the induced variance generalized ordered weighted averaging (Var-IGOWLA) operator. Moreover, this paper analyzes some properties, families and particular cases of the proposed operators. Finally, an illustrative example of the characteristic design of the operators is proposed using real-world information retrieved from financial markets. The objective of this paper is to analyze the performance of some equities based on the expected payoff and the dispersion of its elements. Results show that the equity payoff results present diverse rankings combined with the proposed operators, and the introduced variance measures aid decision-making by offering new tools for information analysis. These results are particularly interesting when selecting logarithmic averaging operators for decision-making processes. The approach presented in this paper extends the available tools for decision-making under ignorance, uncertainty, and subjective environments.