Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem

Predicting black ice-related accidents with probabilistic modeling using GIS-based Monte Carlo simulation

Black ice, a phenomenon that occurs abruptly owing to freezing rain, is difficult for drivers to identify because it mirrors the color of the road. Effectively managing the occurrence of unforeseen accidents caused by black ice requires predicting their probability using spatial, weather, and traffic factors and formulating appropriate countermeasures. Among these factors, weather and traffic exhibit the highest levels of uncertainty. To address these uncertainties, a study was conducted using a Monte Carlo simulation based on random values to predict the probability of black ice accidents at individual road points and analyze their trigger factors. We numerically modeled black ice accidents and visualized the simulation results in a geographical information system (GIS) by employing a sensitivity analysis, another feature of Monte Carlo simulations, to analyze the factors that trigger black ice accidents. The Monte Carlo simulation allowed us to map black ice accident occurrences at each road point on the GIS. The average black ice accident probability was found to be 0.0058, with a standard deviation of 0.001. Sensitivity analysis using Monte Carlo simulations identified wind speed, air temperature, and angle as significant triggers of black ice accidents, with sensitivities of 0.354, 0.270, and 0.203, respectively. We predicted the probability of black ice accidents per road section and analyzed the primary triggers of black ice accidents. The scientific contribution of this study lies in the development of a method beyond simple road temperature predictions for evaluating the risk of black ice occurrences and subsequent accidents. By employing Monte Carlo simulations, the probability of black ice accidents can be predicted more accurately through decoupling meteorological and traffic factors over time. The results can serve as a reference for government agencies, including road traffic authorities, to identify accident-prone spots and devise strategies focused on the primary triggers of black ice accidents.

Goodness-of-fit test for stochastic processes using even empirical moments statistic

In this paper, we introduce a novel framework that allows efficient stochastic process discrimination. The underlying test statistic is based on even empirical moments and generalizes the time-averaged mean-squared displacement framework; the test is designed to allow goodness-of-fit statistical testing of processes with stationary increments and a finite-moment distribution. In particular, while our test statistic is based on a simple and intuitive idea, it enables efficient discrimination between finite- and infinite-moment processes even if the underlying laws are relatively close to each other. This claim is illustrated via an extensive simulation study, e.g., where we confront α-stable processes with stability index close to 2 with their standard Gaussian equivalents. For completeness, we also show how to embed our methodology into the real data analysis by studying the real metal price data.

Goodness-of-fit test for $$\alpha$$-stable distribution based on the quantile conditional variance statistics

The class of $$\alpha$$ α -stable distributions is ubiquitous in many areas including signal processing, finance, biology, physics, and condition monitoring. In particular, it allows efficient noise modeling and incorporates distributional properties such as asymmetry and heavy-tails. Despite the popularity of this modeling choice, most statistical goodness-of-fit tests designed for $$\alpha$$ α -stable distributions are based on a generic distance measurement methods. To be efficient, those methods require large sample sizes and often do not efficiently discriminate distributions when the corresponding $$\alpha$$ α -stable parameters are close to each other. In this paper, we propose a novel goodness-of-fit method based on quantile (trimmed) conditional variances that is designed to overcome these deficiencies and outperforms many benchmark testing procedures. The effectiveness of the proposed approach is illustrated using extensive simulation study with focus set on the symmetric case. For completeness, an empirical example linked to plasma physics is provided.

Omnibus test for normality based on the Edgeworth expansion

Statistical inference in the form of hypothesis tests and confidence intervals often assumes that the underlying distribution is normal. Similarly, many signal processing techniques rely on the assumption that a stationary time series is normal. As a result, a number of tests have been proposed in the literature for detecting departures from normality. In this article we develop a novel approach to the problem of testing normality by constructing a statistical test based on the Edgeworth expansion, which approximates a probability distribution in terms of its cumulants. By modifying one term of the expansion, we define a test statistic which includes information on the first four moments. We perform a comparison of the proposed test with existing tests for normality by analyzing different platykurtic and leptokurtic distributions including generalized Gaussian, mixed Gaussian, α-stable and Student’s t distributions. We show for some considered sample sizes that the proposed test is superior in terms of power for the platykurtic distributions whereas for the leptokurtic ones it is close to the best tests like those of D’Agostino-Pearson, Jarque-Bera and Shapiro-Wilk. Finally, we study two real data examples which illustrate the efficacy of the proposed test.

Identifying diffusive motions in single-particle trajectories on the plasma membrane via fractional time-series models

In this paper we show that an autoregressive fractionally integrated moving average time-series model can identify two types of motion of membrane proteins on the surface of mammalian cells. Specifically we analyze the motion of the voltage-gated sodium channel Nav1.6 and beta-2 adrenergic receptors. We find that the autoregressive (AR) part models well the confined dynamics whereas the fractionally integrated moving average (FIMA) model describes the nonconfined periods of the trajectories. Since the Ornstein-Uhlenbeck process is a continuous counterpart of the AR model, we are also able to calculate its physical parameters and show their biological relevance. The fitted FIMA and AR parameters show marked differences in the dynamics of the two studied molecules.