It is noteworthy that the stretched Gaussian distribution is successfully examined as the fundamental solution of the Hausdorff derivative diffusion equation [7]. Besides, the strategy of Hausdorff calculus by
In one dimension, the Gaussian function is the probability density function of the normal distribution, f(x)=1/(sigmasqrt(2pi))e^(-(x-mu)^2/(2sigma^2)), (1) sometimes also called the frequency curve. The full width at half maximum (FWHM) for a Gaussi
Gaussian probability distribution functionlinear anisotropic scatteringcross-section functionThe stationary solution of the one-speed neutron transport equation in a semi-infinite stochastic medium with linear anisotropic scattering is considered. The cross-section function of the medium is assumed to be a ...
To fit this equation, you need to create rules for initial values. Set the initial value of mean to 1*Xmid. Set the initial value of SD to 0.5*(Xmax-Xmin). Constrain the value of Top a constant value of 1, 100 or N (depending on whether your frequency distribution is expressed as...
\begin{equation}\label{eq:jointdistribution} \begin{bmatrix} \bm{y} \\ f_* \end{bmatrix} \sim \mathcal{N} \left( \begin{bmatrix} \bm{\mu}(X) \\ \bm{\mu}(Z) \end{bmatrix}, \begin{bmatrix} K(X,X) + \sigma^2_n \mathbf{I} \quad K(Z,X)^{\mathrm{T}} \\ K(...
比如BM的kernel是Laplace equation的Green function;feature map是Laplace operator的eigenfunctions。【其实在钟开莱的“Green, Brown, and Probability & Brownian Motion on the Line”也有提到,但目前为止这联系依然是云里雾里。】我们知道Sobolev space是Matern kernel的RKHS,因此linear differential operator Green fn、...
Converging to a Gaussian distribution Surprisingly enough, the equation for a Gaussian distribution can be derived from a uniform distribution. Despite looking quite different, they are deeply connected. Now let’s imagine a scenario in which a drunk man has to walk straight down a line. At ever...
Then equation (2) can be re-written as, Pr(y>x0−μσ)=∫∞(x0−μσ)1√2πe−y22dy(3)Pr(y>x0−μσ)=∫(x0−μσ)∞12πe−y22dy(3) Here the function inside the integral is a normalized gaussian probability density functionY∼N(0,1)Y∼N(0,1), normalized...
Deriving the conditional distribution, we arrive at the key predictive equation for Gaussian process regression f∗|X,y,X∗∼N(¯f∗,cov(f∗))(9)(9)f∗|X,y,X∗∼N(f∗¯,cov(f∗)) where ¯f∗=E[f∗|X,y,X∗]=K(X∗,X)[K(X,X)+σ2nI]−1ycov...
The density plot above can be also described by the equation below, GIF of the process of EM algorithm on GMM (Free GIF from Tenor https://tenor.com/view/gaussian-mixture-models-em-method-math-gauss-computer-science-nerd-gif-15288262) ...