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In statistics, a Kaniadakis distribution (also known as κ-distribution) is a statistical distribution that emerges from the Kaniadakis statistics. [1] 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 ...
The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1). The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a ...
It is one example of a Kaniadakis κ-distribution. The κ-Gaussian distribution has been applied successfully for describing several complex systems in economy, [1] geophysics, [2] astrophysics, among many others. The κ-Gaussian distribution is a particular case of the κ-Generalized Gamma distribution. [3]
Under the null hypothesis of multivariate normality, the statistic A will have approximately a chi-squared distribution with 1 / 6 ⋅k(k + 1)(k + 2) degrees of freedom, and B will be approximately standard normal N(0,1). Mardia's kurtosis statistic is skewed and converges very slowly to the limiting normal distribution.
j=1 a j X j has a (univariate) normal distribution. The variance of X is a k×k symmetric positive-definite matrix V. The multivariate normal distribution is a special case of the elliptical distributions. As such, its iso-density loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids.
In probability theory, particularly information theory, the conditional mutual information [1] [2] is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third.
Z tables use at least three different conventions: Cumulative from mean gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549. Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. Example: Prob(Z ≤ 0.69) = 0.7549. Complementary ...
An equivalent condition for a distribution to be subexponential is then that ‖ ‖ <. [1]: §2.7 Subexponentiality can also be expressed in the following equivalent ways: [ 1 ] : §2.7 P ( | X | ≥ x ) ≤ 2 e − K x , {\displaystyle {\mathbb {P}}(|X|\geq x)\leq 2e^{-Kx},} for all x ≥ 0 {\displaystyle x\geq 0} and some constant K > 0 ...
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