x=0;
% The default values for mu and sigma are 0, 1
% The default values for left and right are 0 Inf
y=tobitpdf(x); 
ynorm=normcdf(x);
assert(y==ynorm,'Tobit density is not correct')
% Pr(Tobit=0, mu=0, sigma=1, left=0, right=Inf) = Pr (Z<0)

x=0; mu=2; sigma=1.5;
% The default values for left and right are 0 Inf
y=tobitpdf(x,mu,sigma); 
ynorm=normcdf(x,mu,sigma);
assert(y==ynorm,'Tobit cdf is not correct')
% Pr(Tobit=0, mu=2, sigma=1.5, left=0, right=Inf) = Pr (Z<0)

x=0; mu=2; sigma=1.5; left=1; right=3;
y=tobitpdf(x,mu,sigma,left,right); 
ynorm=normcdf(x,mu,sigma);
% Pr(Tobit=0, mu=2, sigma=1.5, left=0, right=Inf) = Pr (Z<0)

x=0:10; mu=2; sigma=1.5; left=1; right=3;
y=tobitcdf(x,mu,sigma,left,right); 
ynorm=normpdf(x,mu,sigma);

close all
x=(-3:0.0001:3)';
left=0;
right=2;
mu=0.5;
sigma=1;
x(find(x<left,1,'last'))=NaN;
x(find(x>left,1,'first'))=NaN;
x(find(x<right,1,'last'))=NaN;
x(find(x>right,1,'first'))=NaN;
y=tobitpdf(x,mu,sigma,left,right);
plot(x,y,'LineWidth',2)
hold('on')
stem(left,y(x==left),'Color','b')
stem(right,y(x==right),'Color','b')
title(['Tobit density when \mu=' num2str(mu) ', \sigma=' num2str(sigma) ', ' ...
'left=' num2str(left)  ', right='  num2str(right)])
text(left,tobitpdf(left,mu,sigma,left,right)-0.01, ...
'Pr(Tobit(\mu,\sigma^2,left,right)=left)=\Phi(left,\mu, \sigma^2) ','HorizontalAlignment','right')
text(right,tobitpdf(right,mu,sigma,left,right)+0.01, ...
' Pr(Tobit(\mu,\sigma^2,left,right)=right)=1-\Phi(right, \mu, \sigma^2)','HorizontalAlignment','left')
ylim([0 1])