Bivariate superstatistics: an application to statistical plasma physics

Investigation the Stochastic behaviour of the Traffic Flow: A Case Study of a Section of a Road

“…Maqhrour [6,9,32] used the traffic flow for budapest (Hungary) for the best fit over the collected data and found the normal, exponential, lognormal, gamma and chi-Square are fit using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). DS Berry (1951) used the data and speed for the best relation between the data and speed distribution over the section of road, [11,13,19] studied the superstatistical analysis of traffic flow and found the beta distribution is the best fit with a small fluctuation with chi-square test for the traffic flow data, [18,26] used the traffic data with condition the data is normally distribution and used to check the data is unimodal or a bimodal and found the traffic data follow the unimodal only, [22,30] used to estimate the travel time distribution using all the distribution to estimate the time distribution under the congestion and free flow congestion, [1,24] used the data for superstatistical analysis with best fit data of speed vehicles flow, [23] used the real traffic data and estimate the statistical distributions for forecasting under the uncertainty condition of traffic condition, [5] used the studied the statistical analysis of traffic flow using lognormal distribution of traffic flow, [12] use the time-gap traffic data under the mix-traffic condition and used all the distribution by combining two distribution and also used the goodness-of-fit distribution with hypothesis test, [27] use the time headway and speed headway under the mix condition of traffic flow and test for the statistical analysis using distribution fit, [15,16] studied for the determination of best fit probability distribution of rainfall data in Bangladesh, and test the data under different hypothesis test and distribution technique, [26] use the regression analysis for the fit the probability distribution over the traffic data by considering the traffic data into different types at the location of Hong Kong, [30] used the distribution fit by probability distribution function over the Origin-Destination of traffic network for the congested traffic flow over the considered network and used the Generalized method of Moment with exact and approximate estimator [20] used the goodness-of-fit probability distribution for the traffic data for analysis the traffic network tail and used different hypothesis tests for goodness-of-fit data and Monte Carlo simulation, …”

Transport Equation of Kappa Distributions in the Heliosphere

“…There are multiple mechanisms that can generate kappa distributions in particle systems. Some examples are superstatistics (i.e., the temperature is not fixed but has a special distribution;e.g., Beck & Cohen 2003;Schwadron et al 2010;Hanel et al 2011;Livadiotis 2019a;Gravanis et al 2020;Sánchez et al 2021), effect of shock waves (Zank et al 2006), turbulence (Yoon 2012;Bian et al 2014;Yoon 2014Yoon , 2020, pump acceleration mechanism (Fisk & Gloeckler 2014), colloidal particles (Peterson et al 2013), and polytropes (Meyer-Vernet et al 1995;Livadiotis 2019b).…”

Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem

“…In this sense, non-extensive statistical mechanics offers a more suitable way to characterize systems with non-trivial fluctuations and correlations, which is common in plasmas due to their turbulent behavior and non-linear transport properties [22][23][24][25]. On the other hand, superstatistics is another approach that is not based on generalizing the Boltzmann-Gibbs entropy, but instead proposes the existence of other parameters that follow a distribution different than Boltzmann [21,26,27]. These parameters can be considered effective temperatures in different cells of the plasma, where each cell has a temperature distribution that deviates from a global temperature in a possible thermodynamic equilibrium.…”