function F = frac_default1(F_bar,omega_bar,sigma_bar)

z_bar = norminv(F_bar,0,1);

F = z_bar*sigma_bar - (log(omega_bar) + 0.5*sigma_bar^2);
% mean = -0.5*sigma_bar^2;
% F = F_bar -logncdf(omega_bar,mean,sigma_bar);