API for censored - Incanter 2.0 (in development)

Overview

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

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'

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'

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'

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'

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'

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'

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