brede_pdf_gaussianratio

(export/brede/brede_pdf_gaussianratio.m)

Function Synopsis

p = brede_pdf_gaussianratio(z, sigmaX, sigmaY, muX, muY, rho)

Help text

 brede_pdf_gaussianratio - Gaussian ratio distribution

       p = brede_pdf_gaussianratio(z, sigmaX, sigmaY, muX, muY, rho)
       p = brede_pdf_gaussianratio(z)

       Probability density function for the ratio distribution, 

          z = x/y, 

       where x and y are Gaussian distributed. 

       If x and y have zero mean then the Gaussian ratio distribution
       is the Cauchy distribution. If sigmaY << muY then the Gaussian
       ratio distribution approaches the Gaussian distribution.

       For more general combination of parameters the distribution is
       more complex, and for certain combinations it might even be
       bimodal.

       Example:
         figure % Standardize Cauchy distribution
         z = (-10:0.1:10)';
         plot(z, brede_pdf_cauchy(z), 'y', 'linewidth', 5);
         hold on, plot(z, brede_pdf_gaussianratio(z), 'r:');

         figure % Approach to Gaussian distribution
         z = (-10:0.1:10)';
         semilogy(z, brede_pdf_gauss(z), 'y', 'linewidth', 5);
         hold on, 
         semilogy(z, brede_pdf_gaussianratio(z,1,0.01,0,1), 'r:');

       Reference:
         David V. Hinkley, On the ratio of two correlated normal
           random variables, Biometrika, 56(3):635+, 1969.
         George Marsaglia, Ratios of normal variables and ratios of
           sums of uniform variables, Journal of the American
           Statistical Association, 1965.

       See also: BREDE, BREDE_PDF, BREDE_PDF_CAUCHY,
                 BREDE_PDF_GAUSS. 

 $Id: brede_pdf_gaussianratio.m,v 1.3 2008/05/29 21:21:52 fn Exp $

Cross-Reference Information

brede_mat_kummerexport/brede/brede_mat_kummer.m