Using the Fisher information matrix, we derive an analytical formula for the covariance matrix of the estimates of the basis material projections from photon counting measurements. The derivation assumes Poisson statistics, which is valid if pulse pileup is negligible or the detector electronics ...
The covariance formula is similar to the formula for correlation and deals with the calculation of data points from the average value in a dataset. For example, the covariance between two random variables X and Y can be calculated using the following formula (for population): For a sample cova...
When the covariance between two variables is positive, they tend to move in the same direction. Higher values of one variable tend to correspond with higher values of the other variable. For instance, if we observe a positive covariance between the number of hours spent studying and the corresp...
{for some}\quad \varepsilon >0. \end{aligned}$$ (2) an sgp f is degenerate if its spectral measure consists of a single symmetrised atom \(\rho = \delta ^*_\alpha = \frac{1}{2} (\delta _{\alpha } + \delta _{-\alpha })\) , or equivalently if the covariance is \(r(...
A note on the asymptotic lower bound for the covariance matrix of the GMM estimator of the parameters of agents' utility functions This paper derives under simplifying assumptions an explicit expression for the lower bound on the asymptotic variance of the GMM estimate of the curvature parameter of...
Formula for continuous variables When the two random variables are continuous, the covariance formula involves a double integral: where: is thejoint probability density functionof and ; both the integrals are between and . How to compute the double integral ...
Formula for Portfolio Variance The variance for a portfolio consisting of two assets is calculated using the following formula: Where: wi– the weight of the ith asset σi2– the variance of the ith asset Cov1,2– the covariance between assets 1 and 2 ...
sampled} \\\end{aligned}Covariance=∑Sample Size−1(Retabc−Avgabc)×(Retxyz−Avgxyz)where:Retabc=Day’s return for ABC stockAvgabc=ABC’s average return over the periodRetxyz=Day’s return for XYZ stockAvgxyz=XYZ’s average return over the peri...
We derive an analytical formula for the covariance cov(A,B) of two smooth linear statistics A=[under ∑]ia(λ_{i}) and B=[under ∑]ib(λ_{i}) to leading or... FD Cunden,P Vivo - 《Physical Review Letters》 被引量: 17发表: 2014年 A unified fluctuation formula for one-cut bet...
摘要: We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.DOI: 10.1007/BF00401158 被引量: 30 年份: 1987 ...