|
\right] for | pdf =| cdf = | mean =, otherwise undefined| median =| mode =| variance = | skewness =| kurtosis =| entropy =| mgf =| cf =| }} The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints. It is one example of a Tsallis distribution. The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann–Gibbs entropy or Shannon entropy.〔Tsallis, C. Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years. Braz. J. Phys. 2009, 39, 337–356〕 The normal distribution is recovered as . The q-Gaussian has been applied to problems in the fields of statistical mechanics, geology, anatomy, astronomy, economics, finance, and machine learning. The distribution is often favored for its heavy tails in comparison to the Gaussian for . There is generalized q-analog of the classical central limit theorem in which the independence constraint for the i.i.d. variables is relaxed to an extent defined by the ''q'' parameter, with independence being recovered as ''q'' → 1. In analogy to the classical central limit theorem, an average of such random variables with fixed mean and variance tend towards the q-Gaussian distribution. In the heavy tail regions, the distribution is equivalent to the Student's t-distribution with a direct mapping between q and the degrees of freedom. A practitioner using one of these distributions can therefore parameterize the same distribution in two different ways. The choice of the q-Gaussian form may arise if the system is non-extensive, or if there is lack of a connection to small samples sizes. ==Characterization== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Q-Gaussian distribution」の詳細全文を読む スポンサード リンク
|