The frequency of the first digits of numbers drawn from an exponential probability density oscillate around the Benford frequencies. Analysis, simulations and empirical evidence show that datasets must have at least 10,000 entries for these oscillati...
The stress–strength analysis is investigated for a multicomponent system, where all strength variables of components follow a generalized exponential distribution and are subject to the generalized exponential distributed stress. The estimation...
Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer...
We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are homog...
This paper focuses on applying the Marshall-Olkin approach to generate a new bivariate distribution. The distribution is called the bivariate exponentiated Lomax distribution, and its marginal distribution is the exponentiated Lomax distribution. Num...
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In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions...
In this work, a type II Topp-Leone-G family of distributions is parametrically transformed to create a new flexible family of continuous probability distributions called exponentiated type II Topp-Leone-G distribution through exponentiation. A variet...
Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use o...
This paper aims to describe a statistical model of wrapped densities for bi-invariant statistics on the group of rigid motions of a Euclidean space. Probability distributions on the group are constructed from distributions on tangent spaces and pushe...
The Jensen–Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback–Leibler divergence which measures the total Kullback–Leibler divergence to the average mixture distribution. However, the Jensen–Shan...
Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set Ɛ...
In this paper, a modified exponentiated family of distributions is introduced. The new model was built from a continuous parent cumulative distribution function and depends on a shape parameter. Its most relevant characteristics have been obtained: t...
In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength relia...
In this paper, we propose a new family of distributions, by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new family of distributi...
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 paper investigates the concomitants of order statistics from the bivariate generalized linear exponential (BGLE) distribution. We obtain the probability density function of a single concomitant and the joint probability density function of two c...
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both classical and quantum systems. On the simplex of probability measures, it is proved that the new divergence coincides with the Kullback...
Research in this paper aims to explore the concept of generalized exponentially (
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability...
Exponential families are statistical models which are the workhorses in statistics, information theory, and machine learning, among others. An exponential family can either be normalized subtractively by its cumulant or free energy function, or equiv...
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...
The common approach to wind energy feasibility studies is to use Weibull distribution for wind speed data to estimate the annual energy production (AEP). However, if the wind speed data has more than one mode in the probability density, the conventio...
Future wireless networks are expected to be dense and employ a higher frequency spectrum such as millimeter wave (mmwave) to support higher data rates. In a dense urban environment, the presence of obstructions causes the transmissions between the us...
In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two...
The Jeffreys divergence is a renown arithmetic symmetrization of the oriented Kullback–Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various tec...
By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence. Inspire...
In this study, the authors simulate a polygonal discrete fracture network (DFN) in rock masses. The probability models of the relevant geological parameters, including the orientation, trace length, volume density, and coordinates of the centroid, ar...
In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic pr...
This study introduces a novel one-parameter probability distribution called the QGamma distribution (QGaD), constructed through a specific mixture of the exponential and Chris–Jerry distributions. The mathematical properties of the QGaD are tho...
The continuous Bernoulli distribution is defined on the unit interval and has a unique property related to fractiles. A fractile is a position on a probability density function where the corresponding surface is a fixed proportion. This article prese...
This paper focuses on the non-Gaussian properties of tornado pressure loading on a Texas Tech University (TTU) building model. External pressures of the model were measured at multiple radial positions in a two-celled tornado-like vortex generated by...
This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributio...
The temporal dynamics and statistical characteristics of Raman random fiber lasers are of great significance for studying their physical properties and applications. In this paper, the effect of pump dynamics on the temporal intensity statistical pro...
Probability distributions are very useful in modeling lifetime datasets. However, no specific distribution is suitable for all kinds of datasets. In this study, the bounded truncated Cauchy power exponential distribution is proposed for modeling data...
The Rayleigh distribution is a continuous probability distribution that is inherently asymmetric and commonly used to model right-skewed data. It holds significant importance across a wide range of scientific and engineering disciplines and exhibits...
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one...
The significant fluctuation of industrial electricity consumption has a high impact on power load, which makes the research on recurrence intervals between extreme events of theoretical and practical significance. The study uses a high-frequency data...
We propose a sequential Monte Carlo-based cardinalized probability hypothesis density (SMC-CPHD) filter with adaptive survival probability for multiple frequency tracking to enhance the tracking performance. The survival probability of the particles...
In geometry and topology, a family of probability distributions can be analyzed as the points on a manifold, known as statistical manifold, with intrinsic coordinates corresponding to the parameters of the distribution. Consider the exponential famil...
In this research, we investigate a resistor capacitor electric circuit that exhibits an exponentially decaying transient response. Due to uncertainty in the precise capacitance value, we treat the capacitance as a continuous uniformly distributed ran...
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the le...
Practitioners in all applied domains value simple and adaptable lifetime distributions. They make it possible to create statistical models that are relatively easy to manage. A novel simple lifetime distribution with two parameters is proposed in thi...
The classical exponential (Exp) distribution may have limited capability in describing asymmetric lifetime data and observations with different tail characteristics. In this paper, a new extended exponential model, called the Mixed Exponential–...
In this paper, we apply the double Fourier transform method to the two-dimensional Vlasov equations for a charged particle subjected to white noise, exponentially correlated Gaussian forces, trap forces and thermal and active noises in a magnetic fie...
In a percolating system, there are typically exponentially many spanning paths. Here, we study numerically, for a two-dimensional
The isotropic Cauchy distribution is a member of the central
The paper discusses an extension of the variance-gamma process with stochastic linear drift coefficient. It is assumed that the linear drift coefficient may switch to a different value at the exponentially distributed time. The size of the drift jump...
A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Importa...
The sustainable energy consumption in northeast Asia has a huge impact on regional stability and economic growth, which gives price volatility research in the energy market both theoretical value and practical application. We select China’s fuel oil...
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