How to derive a CDF from a given PDF?

Here is the pdf fucntion: skn = 2.*(1/sqrt(2*pi)).*exp(-0.5*x.^2).*normcdf(a.*x,0,1); How can I define a CDF function from it? Also, after I have CDF, How can I find inverse of that CDF? Thanks.

Answer 1

[Tom Lane]

If you have the Symbolic Toolbox, you might try replacing normcdf by an erf function and see what you get.

Otherwise you could try something like this:

x = linspace(-5,5);
a = pi;
f = @(x) 2.*(1/sqrt(2*pi)).*exp(-0.5*x.^2).*normcdf(a.*x,0,1);
F = zeros(size(x));
for j=1:length(x)
   F(j) = integral(f,-Inf,x(j));
end
plot(x,F)

For the inverse cdf, you might try interpolating or using fzero.