[問題] binomial test for median
要找中位數的信賴區間 (前言有點長，問題在後面)
Ho: θ_0.5 = θ_0
Ha: θ_0.5 > θ_0
B = numbers of {Xi | Xi > θ_0}
P( a ≦ B ≦ b-1) = 1 - α
for large samples , use normal approximation.
P( a-0.5n/(0.25n)^0.5 ≦ B-0.5n/(0.25n)^0.5 ≦ b-1-0.5n/(0.25n)^0.5) ~= 1 - α
a-0.5n/(0.25n)^0.5 ~= -Z_1-α/2
b-1-0.5n/(0.25n)^0.5 ~= Z_1-α/2
四捨五入後的(a , b) 即為信賴區間
問題來了
書上說這是binomail test用常態去近似，所以會加上矯正項，然後取高斯符號來求
a= [ 0.5n-(Z_1-α/2)*(0.25n)^0.5 + 0.5 ]
b= [ 1+ 0.5n-(Z_1-α/2)*(0.25n)^0.5 - 0.5 ] + 1
↗
黃色部份是矯正項沒錯吧? ↗
↗
那為甚麼在計算上界的b時，要加上 1? →
這跟取高斯符號有關嗎@@
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