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Kaniadakis Gaussian Distribution
The Kaniadakis Gaussian distribution (also known as ''κ''-Gaussian distribution) is a probability distribution which arises as a generalization of the Gaussian distribution from the maximization of the Kaniadakis entropy under appropriated constraints. It is one example of a Kaniadakis ''κ''-distribution. The κ-Gaussian distribution has been applied successfully for describing several complex systems in economy, geophysics, astrophysics, among many others. The κ-Gaussian distribution is a particular case of the κ-Generalized Gamma distribution. Definitions Probability density function The general form of the centered Kaniadakis ''κ''-Gaussian probability density function is: : f_(x) = Z_\kappa \exp_\kappa(-\beta x^2) where , \kappa, 0 is the scale parameter, and : Z_\kappa = \sqrt \Bigg( 1 + \frac\kappa \Bigg) \frac is the normalization constant. The standard Normal distribution is recovered in the limit \kappa \rightarrow 0. Cumulative distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shape Parameter
In probability theory and statistics, a shape parameter (also known as form parameter) is a kind of numerical parameter of a parametric family of probability distributionsEveritt B.S. (2002) Cambridge Dictionary of Statistics. 2nd Edition. CUP. that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter). Such a parameter must affect the ''shape'' of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). For example, "peakedness" refers to how round the main peak is. Estimation Many estimators measure location or scale; however, estimators for shape parameters also exist. Most simply, they can be estimated in terms of the higher moments, using the method of moments, as in the ''skewness'' (3rd moment) or ''kurtosis'' (4th moment), if the higher moments are defined and finite. Estimators of shape often involve higher-order statistics (non-linear fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extreme Value Theory
Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood. Similarly, for the design of a breakwater, a coastal engineer would seek to estimate the 50-year wave and design the structure accordingly. Data analysis Two main approaches exist for practical extreme value analysis. The first method relies on deriving block maxima (minima) series as a preliminary step. In many situations it is customary and convenient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaniadakis Erlang Distribution
The Kaniadakis Erlang distribution (or κ-Erlang Gamma distribution) is a family of continuous statistical distributions, which is a particular case of the κ-Gamma distribution, when \alpha = 1 and \nu = n = positive integer. The first member of this family is the κ-exponential distribution of Type I. The κ-Erlang is a κ-deformed version of the Erlang distribution. It is one example of a Kaniadakis distribution. Characterization Probability density function The Kaniadakis ''κ''-Erlang distribution has the following probability density function: : f_(x) = \frac \prod_^n \left 1 + (2m -n)\kappa \rightx^ \exp_\kappa(-x) valid for x \geq 0 and n = \textrm \,\,\textrm , where 0 \leq , \kappa, < 1 is the entropic index associated with the Kaniadakis entropy. The ordinary [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaniadakis Weibull Distribution
The Kaniadakis Weibull distribution (or ''κ''-Weibull distribution) is a probability distribution arising as a generalization of the Weibull distribution. It is one example of a Kaniadakis ''κ''-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of complex systems in seismology, economy, epidemiology, among many others. Definitions Probability density function The Kaniadakis ''κ''-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: : f_(x) = \frac \exp_\kappa(-\beta x^\alpha) valid for x \geq 0, where , \kappa, 0 is the scale parameter, and \alpha > 0 is the shape parameter or Weibull modulus. The Weibull distribution is recovered as \kappa \rightarrow 0. Cumulative distribution function The cumulative distribution function of ''κ''-Weibull distribution is given byF_\kappa(x) = 1 - \exp_\kappa(-\beta x^\alpha) valid for x \geq 0. The cumulative Weibul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaniadakis Distribution
In statistics, a Kaniadakis distribution (also known as κ-distribution) is a statistical distribution that emerges from the Kaniadakis statistics. There are several families of Kaniadakis distributions related to different constraints used in the maximization of the Kaniadakis entropy, such as the κ-Exponential distribution, κ-Gaussian distribution, Kaniadakis κ-Gamma distribution and κ-Weibull distribution. The κ-distributions have been applied for modeling a vast phenomenology of experimental statistical distributions in natural or artificial complex systems, such as, in epidemiology, quantum statistics, in astrophysics and cosmology, in geophysics, in economy, in machine learning. The κ-distributions are written as function of the κ-deformed exponential, taking the form : f_i=\exp_(-\beta E_i+\beta \mu) enables the power-law description of complex systems following the consistent κ-generalized statistical theory., where \exp_(x)=(\sqrt+\kappa x)^ is the Kani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Giorgio Kaniadakis
Kaniadakis Giorgio ( el, Κανιαδάκης Γεώργιος; born on 5 June 1957 in Chania-Crete, Greece) a Greek-Italian physicist, is a Full Professor of Theoretical Physics at Politecnico di Torino (Italy) and is credited with introducing the concept oKaniadakis entropyand what is known as Kaniadakis statistics. He is in thWorld's Top 1% Scientists( Stanford University - Scopus Database), 2022. "Giorgio Kaniadakis has pioneered the surpassing of Boltzmann's Stosszahlansatz within special relativity and proposes a new entropy, emerging as the relativistic generalization of the Boltzmann entropy. Kaniadakis entropy generates power law-tailed distributions, which in the classical limit reduce to the Maxwell-Boltzmann exponential distribution" (From the Editorial by T. Biro of the volume Eur. Phys. J. A 40, N. 3, pp 255-256, 2009) Education In 1975 Giorgio Kaniadakis moved to Italy where he obtained the Bachelor's and Master's degrees in Nuclear Engineering in 1981 from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Langmuir Waves
Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency only depends weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon. Langmuir waves were discovered by American physicists Irving Langmuir and Lewi Tonks in the 1920s. They are parallel in form to Jeans instability waves, which are caused by gravitational instabilities in a static medium. Mechanism Consider an electrically neutral plasma in equilibrium, consisting of a gas of positively charged ions and negatively charged electrons. If one displaces by a tiny amount an electron or a group of electrons with respect to the ions, the Coulomb force pulls the electrons back, acting as a restoring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electroacoustics
Acoustical engineering (also known as acoustic engineering) is the branch of engineering dealing with sound and vibration. It includes the application of acoustics, the science of sound and vibration, in technology. Acoustical engineers are typically concerned with the design, analysis and control of sound. One goal of acoustical engineering can be the reduction of unwanted noise, which is referred to as noise control. Unwanted noise can have significant impacts on animal and human health and well-being, reduce attainment by students in schools, and cause hearing loss. Noise control principles are implemented into technology and design in a variety of ways, including control by redesigning sound sources, the design of noise barriers, sound absorbers, suppressors, and buffer zones, and the use of hearing protection (earmuffs or earplugs). Besides noise control, acoustical engineering also covers positive uses of sound, such as the use of ultrasound in medicine, programming digit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma (physics)
Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the four fundamental states of matter. It contains a significant portion of charged particles – ions and/or s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedmann–Lemaître–Robertson–Walker Metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are customarily grouped as Friedmann or Friedmann–Robertson–Walker (FRW) or Robertson–Walker (RW) or Friedmann–Lemaître (FL). This model is sometimes called the ''Standard Model'' of modern cosmology, although such a description is also associated with the further developed Lambda-CDM mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
