deltazBar = a(u-zBar)+epsilon
Δ z ¯ = a ( u − z ¯ ) + ϵ {\displaystyle \Delta {\overline {z}}=a(u-{\overline {z}})+\epsilon }
Deltazbar = covariance term + transmission term = Cov(w / wbar,z) + E((w / wbar) Deltaz)
Δ z ¯ = covariance term + transmission term = c o v ( w / w ¯ , z ) + E ( ( w / w ¯ ) Δ z ) {\displaystyle {\begin{array}{ll}\Delta {\overline {z}}&={\text{covariance term}}+{\text{transmission term}}\\&=\mathrm {cov} (w/{\overline {w}},z)+\mathrm {E} ((w/{\overline {w}})\Delta z)\end{array}}}
Just Delta zBar and Delta z wBar
Δ z ¯ {\displaystyle \Delta {\overline {z}}}
Δ z {\displaystyle \displaystyle \Delta z}
w ¯ {\displaystyle \displaystyle {\overline {w}}} z ¯ {\displaystyle \displaystyle {\overline {z}}} w {\displaystyle \displaystyle w} z {\displaystyle \displaystyle z}
zbar_O - zbar_P
z O {\displaystyle \displaystyle z_{O}} z P {\displaystyle \displaystyle z_{P}} z ¯ O − z ¯ P {\displaystyle {\overline {z}}_{O}-{\overline {z}}_{P}}
beta(w,z) β ( w , z ) {\displaystyle \displaystyle \beta (w,z)} β ( w , C L ) {\displaystyle \displaystyle \beta (w,{\mathsf {CL}})} β ( w , R ) {\displaystyle \displaystyle \beta (w,{\mathsf {R}})}
Mbar_t = u +(Mbar_0 – u) e-at
M ¯ t = u + ( M ¯ 0 − u ) e − a t {\displaystyle {\overline {M}}_{t}=u+({\overline {M}}_{0}-u)e^{-at}} M ¯ 0 {\displaystyle {\overline {M}}_{0}} M ¯ t {\displaystyle {\overline {M}}_{t}} a {\displaystyle \displaystyle a}
z ¯ 0 {\displaystyle {\overline {z}}_{0}}
zbar_t = u + (zbar_0 – u)e^-at
z ¯ t = u + ( z ¯ 0 − u ) e − a t {\displaystyle {\overline {z}}_{t}=u+({\overline {z}}_{0}-u)e^{-at}}
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