# API for censored - Incanter1.5.5 (stable)

Full namespace name: incanter.censored

## Overview

Statistical functions for work with 'censored' (truncated) distributions.

## censored-mean-lower

function
Usage: (censored-mean-lower a mu sigma)
Returns the mean of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a'

Source

## censored-mean-two-sided

function
Usage: (censored-mean-two-sided a b mu sigma)
Returns the mean of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a' and the upper
tail censored at 'b'

Source

## censored-mean-upper

function
Usage: (censored-mean-upper b mu sigma)
Returns the mean of a normal distribution (with mean mu and standard
deviation sigma) with the upper tail censored at 'b'

Source

## censored-variance-lower

function
Usage: (censored-variance-lower a mu sigma)
Returns the variance of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a'

Source

## censored-variance-two-sided

function
Usage: (censored-variance-two-sided a b mu sigma)
Returns the variance of a normal distribution (with mean mu and standard
deviation sigma) with the lower tail censored at 'a' and the upper
tail censored at 'b'

Source

## censored-variance-upper

function
Usage: (censored-variance-upper b mu sigma)
Returns the variance of a normal distribution (with mean mu and standard
deviation sigma) with the upper tail censored at 'b'

Source

## truncated-variance

function
Usage: (truncated-variance & {:keys [mean sd a b], :or {mean 0, sd 1, a NEGATIVE_INFINITY, b POSITIVE_INFINITY}})
Returns the variance of a normal distribution truncated at a and b.

Options:
:mean (default 0) mean of untruncated normal distribution
:sd (default 1) standard deviation of untruncated normal distribution
:a (default -infinity) lower truncation point
:b (default +infinity) upper truncation point

Examples:

(use '(incanter core stats))
(truncated-variance :a -1.96 :b 1.96)
(truncated-variance :a 0)
(truncated-variance :b 0)

(use 'incanter.charts)
(def x (range -3 3 0.1))
(def plot (xy-plot x (map #(truncated-variance :a %) x)))
(view plot)
(add-lines plot x (map #(truncated-variance :b %) x))

(def samp (sample-normal 10000))
(add-lines plot x (map #(variance (filter (fn [s] (> s %)) samp)) x))
(add-lines plot x (map #(variance (mult samp (indicator (fn [s] (> s %)) samp))) x))

References:
DeMaris, A. (2004) Regression with social data: modeling continuous and limited response variables.
Wiley-IEEE.

http://en.wikipedia.org/wiki/Truncated_normal_distribution

Source

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