Returns the mean of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a'
(defn censored-mean-lower
" Returns the mean of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a'
"
([a mu sigma]
(let [a-std (psi a mu sigma)]
(+ (* (cdf-normal a-std) a)
(* (- 1 (cdf-normal a-std))
(+ mu (* sigma (lambda-lower a-std))))))))
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