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    This procedure estimates the one or two dimensional probability density
    function of a given data set.



Calling Sequence

    pdf, X [, Y]


    X: The X-coordinates of the data values.

Optional Input

    Y: The Y-coordinates of the data values (for two dimensional PDFs).

Keyword Parameters

    BANDWIDTH: If set, the procedure modifies the smoothing parameter size
        depending upon the data density near each point. Otherwise, the
        smoothing parameter is not modified.
    C_COLORS: A vector of colour indices for the contoured levels. This
        applies to two dimensional data only).
    CHARSIZE: The size of the text characters. The default is 1.
    COLOR: The colour index of the axes and text. The default is set in
    FILL: If set, the contours are filled. Otherwise, only contour lines are
        plotted. This applies to two dimensional data only.
    NLEVELS: The number of level values for the contour plot. This
        applies to two dimensional data only.
    NOVERBOSE: If set, messages are not printed.
    NOPLOT: If set, the PDF is not plotted.
    [X,Y]RANGE: A 2-element vector containing the minimum and maximum
        [x,y]-coordinates to be plotted.
    SCORE: If set, the procedure calculates the near optimal smoothing
        parameter value. If not set, a value is estimated assuming a
        multivariate Gaussian distribution.
    [MIN,MAX]SCORE: The minimum, maximum input value for the smoothing
        parameter estimation score function. The default is 0.1, 1.0.
    NSCORE: The size (resolution) of the smoothing parameter estimation score
        function. The default is 29 points.
    NPDF: The size (resolution) of the PDF axes. The default is 31 points.
    TITLE: A string containing the title of the plot.
    [X,Y]TITLE: A string containing the label for the X,Y axis.

Optional Output

    FSCORE: The score function for calculating the near optimal smoothing
        parameter value.
    [X,Y]ID: The X, Y coordinate values of the PDF array (or vector).
    PDF: The probability density function array (or vector).




    This procedure uses formulae from Silverman (1986) to estimate the PDF.
    See these references for more information:
    Brunet, G. 1994. Empirical normal-mode analysis of atmospheric data.
      Journal of Atmospheric Sciences, 51, 932-952.
    Kimoto, M., and M. Ghil. 1993. Multiple flow regimes in the Northern
      Hemisphere winter. Part I: Methodology and hemispheric regimes.
      Journal of Atmospheric Sciences, 50, 2625-2643.
    Silverman, B. W. 1986. Density Estimation for Statistics and Data
      Analysis. Chapman and Hall, 175p.


    Create a vector of Gaussian noise.
      x = randomn( seed, 100 )
    Estimate and plot the PDF of the data. Make the best estimate.
      pdf, x, BANDWIDTH=1, SCORE=1

Modification History

    Written by: Daithi Stone (stoned@atm.ox.ac.uk), 2001-05-09
    Modified: DAS, 2001-06-04 (modified the pilot smoothing parameter
    Modified: DAS, 2002-03-15 (modified style, streamlined eta estimator,
        allowed eta estimator in 1D)
    Modified: DAS, 2002-04-10 (switched std.pro to stddev)
    Modified: DAS, 2003-01-30 (minorly optimised score calculation)
    Modified: DAS, 2003-05-28 (added NOVERBOSE keyword)
    Modified: DAS, 2004-08-20 (modified FSCORE to return output even if SCORE
        is not set)
    Modified: DAS, 2005-08-05 (replaced sum.pro use with total)
    Modified: DAS, 2007-05-24 (removed use of constants.pro; changed faulty
        normalisation method to simple calculation)
    Modified: DAS, 2012-01-24 (Edited for compliance with GDL)

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