Manuscript En10-B@1 · En10-B.tex · section · a1105bad

The derived four-outcome law

Likelihood, source sensitivity, and nuisance information › The derived four-outcome law · lines 578–596

En10-B@1#eq:moments, En10-B@1#eq:moment-bounds

Define

t_{k} = (1 - n_{z}^{2}) sin^{2} (ϕ + ξ_{k}), u = k \sum w_{k} t_{k}, v = k \sum w_{k} t_{k}^{2}, d = 1 - 2 u .

The calibration set implies

t_{-} t_{+} t_{-} = (1 - z_{*}^{2}) sin^{2} (ϕ_{0} - ϵ_{ϕ} - κ) > 0, = sin^{2} (ϕ_{0} + ϵ_{ϕ} + κ) < \frac{1}{2}, \leq u \leq t_{+}, d > 0, h = 1 - γ > 0.

Displayed formulas in this passage

En10-B@1#eq:moments · line 581
$t_{k} = (1 - n_{z}^{2}) sin^{2} (ϕ + ξ_{k}), u = k \sum w_{k} t_{k}, v = k \sum w_{k} t_{k}^{2}, d = 1 - 2 u .$
En10-B@1#eq:moment-bounds · line 588
$t_{-} t_{+} t_{-} = (1 - z_{*}^{2}) sin^{2} (ϕ_{0} - ϵ_{ϕ} - κ) > 0, = sin^{2} (ϕ_{0} + ϵ_{ϕ} + κ) < \frac{1}{2}, \leq u \leq t_{+}, d > 0, h = 1 - γ > 0.$