mRosinRammlerSMD( value, spread, dCUP )

function smd = mRosinRammlerSMD( value, spread, dCUP )
%  Calculates Sauter mean diameter for the modified Rosin-Rammler
%  distribution with parameters SPREAD and DCUP, over the range VALUE.
%
%  USAGE:       p = mRosinRammlerSMD(x, q, d)
% 
%  ARGUMENTS:
%      X must be a positive real number or 1-D vector.
%      D (default value: 15.0) must be a scalar.
%      q (default value: 5) must be a scalar, typically between 1.5 and 5.
% 
%  EXAMPLE:
%              x = (5:.1:50);
%              mRosinRammlerSMD(x)
% 
%  SEE ALSO:    MROSINRAMMLERCDF, MROSINRAMMLERPDF, MROSINRAMMLERFIT,
%               MROSINRAMMLERDEMO

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  Modified Rosin-Rammler distribution 
%
%  Y = 1-EXP(-(Ln(X)/Ln(D))^q)
%
%  The distribution is described in terms of 2 parameters, D and q:
%
%   -  D is a representative diameter, commonly chosen such that 63.2% the
%      total volume is contained in particles smaller than D.
%
%   -  The exponent q provides a measure of the spread of drop sizes.  The
%      higher the value of q, the more uniform the spray.  If q is 
%      infinite the drops in the spray are all the same size.  For typical
%      sprays, the value of q is between 1.5 and 4.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    

X = value;
q = spread;
D = dCUP;

% SMD = (x^3 * PDF value)/(x^2 * PDF value)
numerator = sum(X.^3 .* mRosinRammlerPDF(X,q,D));
denominator = sum(X.^2 .* mRosinRammlerPDF(X,q,D));
smd = numerator/denominator;