MMM

       Estimate the sky background in a stellar contaminated field.

       MMM assumes that contaminated sky pixel values overwhelmingly display
       POSITIVE departures from the true value.  Adapted from DAOPHOT
       routine of the same name.

       MMM, sky, [ skymod, sigma, skew, HIGHBAD = , READNOISE=, /DEBUG,
                  NSKY=, /INTEGER]

       SKY - Array or Vector containing sky values.  This version of
               MMM does not require SKY to be sorted beforehand.  SKY
               is unaltered by this program.

       skymod - Scalar giving estimated mode of the sky values
       SIGMA -  Scalar giving standard deviation of the peak in the sky
               histogram.  If for some reason it is impossible to derive
               skymod, then SIGMA = -1.0
       SKEW -   Scalar giving skewness of the peak in the sky histogram
               If no output variables are supplied or if /DEBUG is set
               then the values of skymod, SIGMA and SKEW will be printed.

       HIGHBAD - scalar value of the (lowest) "bad" pixel level (e.g. cosmic
                rays or saturated pixels) If not supplied, then there is
                assumed to be no high bad pixels.
       READNOISE - Scalar giving the read noise (or minimum noise for any
                pixel).     Normally, MMM determines the (robust) median by
                averaging the central 20% of the sky values.     In some cases
                where the noise is low, and pixel values are quantized a
                larger fraction may be needed.    By supplying the optional
                read noise parameter, MMM is better able to adjust the
                fraction of pixels used to determine the median.
       /INTEGER - Set this keyword if the  input SKY vector only contains
                discrete integer values.    This keyword is only needed if the
                SKY vector is of type float or double precision, but contains
                only discrete integer values.     (Prior to July 2004, the
                equivalent of /INTEGER was set for all data types)
       /DEBUG - If this keyword is set and non-zero, then additional
               information is displayed at the terminal.

      NSKY - Integer scalar giving the number of pixels actually used for the
             sky computation (after outliers have been removed).

       (1) Program assumes that low "bad" pixels (e.g. bad CCD columns) have
       already been deleted from the SKY vector.
       (2) MMM was updated in June 2004 to better match more recent versions
       of DAOPHOT.
       (3) Does not work well in the limit of low Poisson integer counts
       (4) MMM may fail for strongly skewed distributions.

       The algorithm used by MMM consists of roughly two parts:
       (1) The average and sigma of the sky pixels is computed.   These values
       are used to eliminate outliers, i.e. values with a low probability
       given a Gaussian with specified average and sigma.   The average
       and sigma are then recomputed and the process repeated up to 20
       iterations:
       (2) The amount of contamination by stars is estimated by comparing the
       mean and median of the remaining sky pixels.   If the mean is larger
       than the median then the true sky value is estimated by
       3*median - 2*mean

       Adapted to IDL from 1986 version of DAOPHOT in STSDAS,
       W. Landsman, STX Feb 1987
       Adapted for IDL Version 2, J. Isensee, STX, Sept 1990
       Added HIGHBAD keyword, W. Landsman January, 1991
       Fixed occasional problem with integer inputs    W. Landsman  Feb, 1994
       Avoid possible 16 bit integer overflow   W. Landsman  November 2001
       Added READNOISE, NSKY keywords,  new median computation
                          W. Landsman   June 2004
       Added INTEGER keyword W. Landsman July 2004
       Improve numerical precision  W. Landsman  October 2004

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