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       log:  c:\Imbook\bwebpage\Section3\mma12p3draws.txt
  log type:  text
 opened on:  18 May 2005, 21:48:36

. 
. ********** OVERVIEW OF MMA12P3DRAWS.DO **********
. 
. * STATA Program 
. * copyright C 2005 by A. Colin Cameron and Pravin K. Trivedi 
. * used for "Microeconometrics: Methods and Applications" 
. * by A. Colin Cameron and Pravin K. Trivedi (2005)
. * Cambridge University Press 
. 
. * Chapter 12.8.2 pages 412-5
. * Draws figures that illustrate two common ways to draw random variates
. 
. * (1) Illustrate Inverse Transformation method: Figure 12.2
. * (2) Illustrate Envelope method: Figure 12.3
. 
. * No data need be read in.
. 
. ********** SETUP **********
. 
. set more off

. version 8

. set scheme s1mono

.   
. ********** (1) INVERSE TRANSFORMATION - FIGURE 12.2 page 413 **********
. 
. * Graph is for x = 0 to 5 in increments of 0.05
. set obs 100
obs was 0, now 100

. gen x = 0.05*_n

. * Unit Exponential cdf
. gen Fx = 1 - exp(-x) 

. * Suppose uniform draw is 0.64
. gen uniformdraw = 0.64

. 
. graph twoway (line Fx x, yline(0.64) xline(1.02)),  /*
>   */ scale (1.2) plotregion(style(none)) /*
>   */ title("Inverse Transformation Method") /*
>   */ xtitle("Random variable x", size(medlarge)) xscale(titlegap(*5)) /*
>   */ ytitle("Cdf  F(x)", size(medlarge)) yscale(titlegap(*5)) /*
>   */ caption(" " "Draw of 0.64 (vertical axis) yields x = 1.02 (horizontal axis).")

. graph save ch12fig2invtransform, replace
(file ch12fig2invtransform.gph saved)

. graph export ch12fig2invtransform.wmf, replace
(file c:\Imbook\bwebpage\Section3\ch12fig2invtransform.wmf written in Windows Metafile format)

. 
. ********** (2) ENVELOPE METHOD - FIGURE 12.3 **********
. 
. * The following is a modification of the figure in the book
. * making clear that the envelope is a scaling up of g(x)
. 
. clear

. 
. * Graph is for x = 0 to 10 in increments of 0.1
. set obs 101
obs was 0, now 101

. gen x = -0.05 + 0.1*_n

. * Unit Exponential cdf
. gen fx = normden(x-4)

. gen gx = 1.5*normden(x-4)+0.005

. 
. graph twoway (line fx x, clstyle(p1)) /*
>   */ (line gx x, clstyle(p1) clwidth(*2) clcolor(gs12)), /*
>   */ scale (1.2) plotregion(style(none)) /*
>   */ title("Accept-reject Method") /*
>   */ xtitle("Random variable x", size(medlarge)) xscale(titlegap(*5)) /*
>   */ ytitle("f(x) and kg(x)", size(medlarge)) yscale(titlegap(*5)) /*
>   */ legend(pos(1) ring(0) col(1)) legend(size(small)) /*
>   */ legend( label(1 "Desired density f(x)") label(2 "Envelope kg(x)") )

. graph save ch12fig3envelope, replace
(file ch12fig3envelope.gph saved)

. graph export ch12fig3envelope.wmf, replace
(file c:\Imbook\bwebpage\Section3\ch12fig3envelope.wmf written in Windows Metafile format)

. 
. ********** CLOSE OUTPUT **********
. log close
       log:  c:\Imbook\bwebpage\Section3\mma12p3draws.txt
  log type:  text
 closed on:  18 May 2005, 21:48:42
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