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Numerical Inversion of a Bivariate Characteristic Function

version 1.24 (161 KB) by Viktor Witkovsky
cf2Dist2D is a MATLAB algorithm for numerical inversion of a bivariate characteristic function which evaluates PDF and CDF from bivariate CF


Updated 14 Apr 2021

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cf2Dist2D calculates the CDF and PDF from the BIVARIATE characteristic function CF by using the Gil-Pelaez inversion formulae and the Riemann quadrature sum, as suggested in Shephard (1991).

The algorithm cf2Dist2D is a part of the MATLAB toolbox CharFunTool:

result = cf2Dist2D(cf,x)

EXAMPLE 1 (CDF/PDF of bivariate standard normal distribution)
cf = @(t) exp(-(0.9*t(:,1).^2 + 0.3*t(:,2).^2 +2*0.4*t(:,1).*t(:,2))/2);
result = cf2Dist2D(cf)
disp([result.x result.cdf])

% EXAMPLE 2 (CDF/PDF of a mixture of bivariate logistic distributions)
mu1 = [0 2];
beta1 = [1 2];
cf1 = @(t) cf2D_Logistic(t,mu1,beta1);
mu2 = [2 1];
beta2 = [2 1];
cf2 = @(t) cf2D_Logistic(t,mu2,beta2);
cf = @(t) 0.25*cf1(t) + 0.75*cf2(t);
options.xN = 51;
result = cf2Dist2D(cf,[],options)

Cite As

Viktor Witkovsky (2021). Numerical Inversion of a Bivariate Characteristic Function (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2020a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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