. . , p, and tij , i > j, has a real scalar Gaussian distribution with mean value zero and variance σ 2, that is, tij i∼id N (0, σ 2) for all i > j . 342 Arak M. Mathai, Serge B. Provost, Hans J. Haubold 5.5
For example, if 𝑤(𝑥)=1+(1−𝛼(𝑥−𝜇)𝜎)2w(x)=1+1−α(x−μ)σ2,𝛼∈ℝα∈R, and 𝑓(𝑥)f(x) is the pdf of the normal distribution with mean 𝜇∈ℝμ∈R and variance 𝜎2>0σ2>0, then (2) reduces to the family of bimodal distributions ...
,xS)′, investing the rest of their wealth at the risk-free return rf, to maximize their utility:(1)maxx′(Et(Pt+1+δt+1)−(1+rf)Pt)−γi2x′Ωtx,where Pt is the vector of prices at time t, Ωt is the variance–covariance matrix of Pt+1+δt+1, and γi is agent i...
extending the beta-binomial distribution. Our solution allows to obtain all possible variances for a discrete distribution defined on{1,…,M}. Our method also provides a reparameterisation to obtain easy to interpret parametersψ(mean value) andρ(confidence level linearly dependent on variance). ...
The moments of the beta distribution are (A.76)〈xn〉≡∫01xnf(x)dx=∏i=0n−1α+iα+β+i, from which the mean value is (A.77)μ≡〈x〉=αα+β, and the variance is (A.78)σ2≡〈x2〉−μ2=αβ(α+β)2(α+β+1). Examples of the beta function are shown in Fig...
Horizontal bars show the mean and two-sided, paired t test was calculated (*p < 0.05, **p < 0.01). c Representative microscopic pictures of tumor cell migration induced by conditioned media from m2c-MDM (donor 11) untransfected or transfected with control siRNA or TGFBI siRNA. Full...
distribution as r grows large. Lemma 2.3. Let r > 0, and let X be a variable with distribution χ r . Then as r→∞ the distribution of X− √ r converges to a normal distribution of mean 0 and variance 1/2. Proof. We prove this lemma by looking at the density function of χ...
This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 262 Lipid Metabolism 2. ...
Monocytes incubated for 16 h without LPS produced 9.6 ± 0.9 nmol of superoxide per million cells, whereas monocytes primed with LPS produced 20.0 ± 1.0 nmol (mean ± SE, n = 4, P < 0.001 by ANOVA). (Even under these endotoxin-free, non-adherent culture conditions, monocytes become ...
Statistical analysis Statistical analysis was conducted using the Statistical Package for the Social Sciences software version 26.0, and the data were presented as mean ± standard devia- tion. The independent samples t-test was used to com- pare two groups, and one-way analysis of variance was ...