104 Results Found

The Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent the usual states of a system after a repair: as new, as old, or in a condition between new and old. It is often coupled with the Weibull distribu...

Modeling financial markets based on empirical data poses challenges in selecting the most appropriate models. Despite the abundance of empirical data available, researchers often face difficulties in identifying the best fitting model. Long-range mem...

In this paper, we investigate the inter-event times of frequent words observed in 17 academic books, where the inter-event time is defined as the number of sentences between two successive appearances of a given word. Our results show that the distri...

The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributi...

We show that the configurational probability distribution of a classical gas always belongs to the q-exponential family. One of the consequences of this observation is that the thermodynamics of the configurational subsystem is uniquely determined up...

Non-extensive statistical mechanics (NESM), which is a generalization of the traditional Boltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating the irreversible damage evolution processes and fracture mechanisms o...

In the theory of complex systems, long tailed probability distributions are often discussed. For such a probability distribution, a deformed expectation with respect to an escort distribution is more useful than the standard expectation. In this pape...

This paper introduces a q-deformed extension of the Lindley distribution. This extension is obtained by replacing the classical exponential with the q-exponential function from Tsallis non-extensive statistical techniques. This transformation offers...

For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distributi...

We give two arguments why the thermodynamic entropy of non-extensive systems involves R´enyi’s entropy function rather than that of Tsallis. The first argument is that the temperature of the configurational subsystem of a mono-atomic gas is equal to...

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of t...

In non-equilibrium plasmas, the temperature cannot be uniquely determined unless the energy-distribution function is approximated as a Maxwell–Boltzmann distribution. To overcome this problem, we applied Tsallis statistics to determine the temp...

We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussia...

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were generalized, three decades ago, on the basis of the nonadditive entropy $S_q$ ( $q\in \mathcal{R}$ ), which recovers the BG entropy in the $q\to 1$ limit. The optimiza...

The Yellowstone Park volcanic field is one of the most active volcanic systems in the world, presenting intense seismic activity that is characterized by several earthquake swarms over the last decades. In the present work, we focused on the spatiote...

Greece exhibits the highest seismic activity in Europe, manifested in intense seismicity with large magnitude events and frequent earthquake swarms. In the present work, we analyzed the spatiotemporal properties of recent earthquake swarms that occur...

We investigate solutions of a generalized diffusion equation that contains nonlinear terms in the presence of external forces and reaction terms. The solutions found here can have a compact or long tail behavior and can be expressed in terms of the q...

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means o...

In the volcanic complex processes, inherent long-range interactions exist suggesting that Non-Extensive Statistical mechanics could be used to describe fundamental properties of the system. Based on the non-extensive Tsallis entropy a frequency-volum...

The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the considera...

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seis...

The probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has b...

Several generalizations or extensions of the Boltzmann–Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies $S_q\equiv k$...

This paper proposes a method for the beta pricing model under the consideration of non-Gaussian returns by means of a generalization of the mean-variance model and the use of principal curves to define a divergence model for the optimization of the p...

The kappa distributions, or their equivalent, the q-exponential distributions, are the natural generalization of the classical Boltzmann-Maxwell distributions, applied to the study of the particle populations in collisionless space plasmas. A huge s...

We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the...

In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which ar...

This paper develops a two-variable truncated-exponential-based Hahn–Appell polynomial family of order r in quantum q-calculus, generated by $\mathcal{A}\left(t\right){(1-\eta t^r)}^{-1}{e}_q^{wt}\left(\zeta t\right)$, where $\mathcal{A}\left(t\right)$ is a normalized determining function and $e_q^{wt}$ den...

Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann–Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implement...

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential...

We numerically study the first-principle dynamics and thermostatistics of a d-dimensional classical inertial Heisenberg ferromagnetic model ( $d=1,2,3$ ) with interactions decaying with the distance $r_{ij}$ as $1/r_{ij}^{\mathrm{\&alph}}$...

On 2 December 2020, an earthquake with a magnitude of M_w 4.5 occurred near the city of Thiva (Greece). The aftershock sequence, triggered by ruptures on or near the Kallithea fault, continued until January 2021. Seven months later, new seismic activi...

This article describes the study of wormhole solutions in $f\left(Q\right)$ gravity with noncommutative geometry. Here, we considered two different $f\left(Q\right)$ models—a linear model $f\left(Q\right)=\alpha Q$ and an exponential model $f\left(Q\right)=Q-\alpha \left(1-e^{-Q}\right)$, where Q is the non-metricity and $\alpha$ is th...

In many Bayesian computations, we first obtain the expression of the joint distribution of all the unknown variables given the observed data. In general, this expression is not separable in those variables. Thus, obtaining the marginals for each vari...

This paper investigates the long-term behavior of diffusion models in population dynamics before absorption. By establishing the intrinsic ultracontractivity of the associated Markov semigroups, we obtain sharp quantitative estimates for three fundam...

From an information geometric perspective, this study considers a natural foliation of dualistic structures associated with escort distributions of exponential families. We propose an extended divergence on this foliation by continuous-type escort di...

We introduce a family of pseudorandom binary sequences defined by the truncated sum-of-digits function of squares in base-q with $q\ge 2$. Using the Erdős–Turán inequality and Weyl-type bounds for quadratic exponential sums, we estima...

In the paper, we present an extension of the truncated-exponential skew-normal (TESN) distribution. This distribution is defined as the quotient of two independent random variables whose distributions are the TESN distribution and the beta distributi...

Generalized numbers, arithmetic operators, and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of q-logarithm/q-exponential inverse functions. Some of the objects were previ...

This paper introduces a new family of q-special polynomials, termed q-general Bell polynomials, and systematically explores their structural and analytical properties. We establish their generating functions, derive explicit series representations, a...

Testing exponentiality against increasing failure rate alternatives is central to reliability theory and lifetime data analysis. This paper develops the Adaptive Cumulative Residual Entropy Test under Proportional Hazards (Adaptive CRE-PH Test), a sc...

In recent times, we have encountered new situations that have imposed restrictions on our ability to visit public places. These changes have affected various aspects of our lives, including limited access to supermarkets, vegetable shops, and other e...

We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Regularization methods are popular for the estimation in the normal linear model. However, heavy-t...

Examining the evolution of the maximum of valence quark distribution, $q_V$, weighted by Bjorken x, $h(x,t)\equiv x{q}_V(x,t)$, it is observed that $h(x,t)$ at the peak becomes a one-parameter function; $h(x_p,t)=\Phi \left(x_p\left(t\right)\right)$, where $x_p$ is the position of the peak, $t=log{Q}^2$...

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the syst...

We study exceedance counts for order statistic intervals when boundary uncertainty is modeled through a fuzzy improved distribution function. In an ordinary setting, whether an observation falls below a threshold is decided by a crisp comparison, whi...

A non-linear filtering algorithm based on the alpha-divergence is proposed, which uses the exponential family distribution to approximate the actual state distribution and the alpha-divergence to measure the approximation degree between the two distr...

This article proposes a new lifetime-generated family of distributions called the sine-exponentiated Weibull-H (SEW-H) family, which is derived from two well-established families of distributions of entirely different nature: the sine-G (S-G) and the...

The primary goal of business organization is optimally maximizing their productivity and profit whilst reducing the cost resulting from lost sales and services given to their customers, which can be achieved by exceeding the balance between the deman...

This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary supp...