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