*! version 1.0.0 STB-34 gr20
program define tryrej
	version 5.0

	quietly {
		preserve
		clear
	
		gph open, saving(tryrej1.gph,replace)
	
		set obs 201
		gen x=5*(_n-101)/100
		gen y=sqrt(_pi/2)*exp(-x^2/2)*(1+x^2)
	
		graph y x, c(l) s(i) xlab(-5,-4,-3,-2,-1,0,1,2,3,4,5) ylab /*
			   */ title("N(0,1)/Standard Cauchy")
		gphsave
	
		local c=sqrt(2*_pi)*exp(-.5)
		local dc: display %5.3f `c'
		local oc: display %5.3f 1-(1/`c')
	
		gphdt line `c' -1 0 -1
		gphdt line `c'  1 0  1
		gphdt line   0 -5 0  5
	
		gphdt text `c'  1 0 -1 (1,`dc')
		gphdt text `c' -1 0  1 (-1,`dc')
	
		gph close
		gph open, saving(tryrej2.gph,replace)
	
	*   Graph h(x)=c*g(x):
	
		gen h=`c'/(_pi*(1+x^2))
		graph h x, c(l) s(i) xlab(-5,-4,-3,-2,-1,0,1,2,3,4,5) ylab /*
		           */ title("h(x) and f(x), P(rejection = `oc'")
		gphsave
	
	*   Add N(0,1) curve and shade rejection region:
	
		replace y=exp(-x^2/2)/sqrt(2*_pi)
		gphdt vline y x
		gphdt vpoly y x h x
	
		gph close
	
	}
end