Name

---

ROBUST_SIGMA

Purpose

---

Calculate a resistant estimate of the dispersion of a distribution.

Explanation

---

For an uncontaminated distribution, this is identical to the standard
deviation.

Calling Sequence

---

result = ROBUST_SIGMA( Y, [ /ZERO, GOODVEC = ] )

Input

---

Y = Vector of quantity for which the dispersion is to be calculated

Optional Input Keyword

---

/ZERO - if set, the dispersion is calculated w.r.t. 0.0 rather than the
central value of the vector. If Y is a vector of residuals, this
should be set.
  OPTIONAL OUPTUT KEYWORD:
      GOODVEC = Vector of non-trimmed indices of the input vector

Output

---

ROBUST_SIGMA returns the dispersion. In case of failure, returns
value of -1.0

Procedure

---

Use the median absolute deviation as the initial estimate, then weight
points using Tukey's Biweight. See, for example, "Understanding Robust
and Exploratory Data Analysis," by Hoaglin, Mosteller and Tukey, John
Wiley & Sons, 1983, or equation 9 in Beers et al. (1990, AJ, 100, 32)
  REVSION HISTORY:
H. Freudenreich, STX, 8/90
      Replace MED() call with MEDIAN(/EVEN) W. Landsman December 2001
      Don't count NaN values W.Landsman June 2010