With the tail bound of the Gaussian distribution P[Z-(\frac{1}{2\sigma^2})v^2\geq t(\frac{1}{\sigma})||v||_2]\leq exp(-\frac{t^2}{2})\\ P[Z\geq t(\frac{1}{\sigma})||v||_2+(\frac{1}{2\sigma^2})v^2]\leq exp(-\frac{t^2}{2})\\ Here, we require mo...
Gaussian Distribution In subject area: Biochemistry, Genetics and Molecular Biology GGMs, also known as partial correlation networks, are undirected graphical models in which nodes correspond to variables of interest (such as metabolites) and weighted edges correspond to partial correlations between these...
P(||X||22≤E[||X||22]−t)≤f(t,σ2,n),P(||X||22≤E[||X||22]−t)≤f(t,σ2,n), for some concrete function ff and any positive real number tt? I can show that an upper tail concentration bound exists that looks like: P(||X...
This is calculated by using suitable tail bounds for the chi-squared distribution (see Methods). It is valid for any CM of two correlated systems even if the entries are given theoretically via a model, e.g., y=τx+ϵ, with scale factor τ and variance σϵ2 for the normal ...
Furthermore, in our Value-at-Risk analysis, we find that ignoring the bound cluster in the tail of the distribution could lead to a significant overestimation of the number of violations and produce unreliable Value-at-Risk measures. In addition, we also find that the proposed model has a ...
Algorithm 2 produces a tailcut binary Gaussian distribution, namely a Gaussian distribution D[N1],σ2 with probability density function ρσ2(x)/ρσ2([N1]) over the set of non-negative integers [N1]={0,1,2,…,N1}. Proof In Security analysis One can simply give a constant-time implem...
HereΦ−1(q)denotes the inverse cdf of the standard normal distribution. The mean of the maximum of the sizennormal sample, for largen, is well approximated bymn=√2((γ−1)Φ−1(2−2n)−γΦ−1(2−2en))=√log(n22πlog(n22π))⋅(1+γlog(n)+o(1log(n))) ...
Cramer-Rao lower boundAn extended generalized Gaussian distribution which can describe a family of symmetric and asymmetric distributions is considered. Parameter estimation of this function using maximum likelihood scheme is proposed. By measured the tail length and skewness of the observed data, the ...
1)Gaussian-double exponential distribution高斯-双指数混合分布 1.At the same time, a method to fit the height deviation sample with fixed intervals based on exponential power distribution andGaussian-double exponential distributionis presented to capture the high-peak and fat-tail characteristic of the...
Hence, not a single expansion method is a recognized upfront approach concerning the choice of a particular expansion type and deciding number of terms to consider tail region accuracy. Authors in [40] used Pearson distribution functions to approximate distributions of power flows. Maximum entropy ...