.
.  Starting Uniform Random Numbers Case Study
.
. Setting Dataplot defaults
reset data
reset plot control
erase
x3label automatic
dimension 100 variables
tic offset units screen
tic offset 5 5
title displacement 2
case asis
title case asis
label case asis
tic label case asis
character case asis all
legend case asis
.  Finished Setting Defaults
.
. Starting Step 1.1
.
skip 25
set read format 5f10.6
serial read randu.dat y
skip 0
set read format
. Finished Step 1.1: Page Back for Output

. Starting Step 2.1
. Generate 4-plot
.
label size 6
tic label size 6
character size 4
x3label displacement 11
x3label automatic
4-plot Y
x3label
move 50 96
justification center
height 4
text Uniform Random Numbers: 4-PLot
. Finished Step 2.1: Page Back for Output

. Starting Step 3.1
.
y1label y
x1label index
plot y
. Finished Step 3.1: Page Back for Output

. Starting Step 3.2
.
y1label y( i )
x1label y(i-1)
line blank
char x
lag plot y
. Finished Step 3.2: Page Back for Output

. Starting Step 3.3
.
y1label Rlc()elative uc()Flc()requency
x1label Y
let s = standard deviation y
let xmean = mean y
x2label lc()mean = ^xmean, sd = ^s
x3label
let a = 0.3*s
let xmin = minimum y
let xmax = maximum y
class upper xmax
class lower xmin4
legend 1 Clc()lass uc()wlc()idth = ^a
relative histogram y
limits freeze
legend 1
pre-erase off
line solid
character blank
plot norpdf(x,xmean,s) for x = xmin 0.01 xmax
pre-erase on
limits
x2label
. Finished Step 3.3: Page Back for Output

. Starting Step 3.4
.
y1label Rlc()elative uc()Flc()requency
x1label Y
x2label Ulc()niform uc()PDF: lc()from 0 to 1
x3label
let a = 0.3*s
let xmin = minimum y
let xmax = maximum y
class upper xmax
class lower xmin4
legend 1 Clc()lass uc()wlc()idth = ^a
relative histogram y
limits freeze
legend 1
pre-erase off
line solid
character blank
plot unipdf(x) for x = 0 0.1 1
pre-erase on
limits
x2label
. Finished Step 3.4: Page Back for Output

. Starting Step 3.5
.
y1label Dlc()ata
x1label Tlc()heoretical
char circle
char hw 1 0.75
line blank
normal probability plot y
let x1 = -1.7
let y1 = ppa0 + ppa1*x1
let xn = 2.5
let yn = ppa0 + ppa1*xn
character blank
line solid
limits freeze
pre-erase off
let xjunk = data x1 xn
let yjunk = data y1 yn
plot yjunk xjunk
limits
pre-erase on
justification center
move 50 4
text Flc()itted uc()llc()ine: uc()Ilc()ntercept = ^PPA0, uc()Slc()lope = ^ppa1
delete x1 y1
. Finished Step 3.5: Page Back for Output

. Starting Step 3.6
.
x3label
title ulc()niform uc()plc()robability uc()plc()lot
x3label
y1label Dlc()ata
x1label Tlc()heoretical
char circle
char hw 1 0.75
line blank
uniform probability plot y
let x1 = xplot(1)
let y1 = ppa0 + ppa1*x1
let n = size xplot
let xn = xplot(n)
let yn = ppa0 + ppa1*xn
line solid
character blank
drawdata x1 y1 xn yn
justification center
move 50 4
text Flc()itted uc()llc()ine: uc()Ilc()ntercept = ^PPA0, uc()Slc()lope = ^ppa1
delete x1 y1
. Finished Step 3.6: Page Back for Output

. Starting Step 4.1
. Generate bootstrap plots
.
x3label
title size 6
label size 6
tic label size 6
x2label size 7
multiplot 2 3
multiplot corner coordinates 0 0 100 100
major xtic mark number 3
title Bootstrap Mean Plot
bootstrap mean plot y
let a1 = b025
let a1 = round(a1,2)
let a2 = b975
let a2 = round(a2,2)
let y1 = yplot
title Bootstrap Median Plot
bootstrap median plot y
let y2 = yplot
let b1 = b025
let b1 = round(b1,2)
let b2 = b975
let b2 = round(b2,2)
title Bootstrap Midrange Plot
bootstrap midrange plot y
title
let y3 = yplot
let c1 = b025
let c1 = round(c1,3)
let c2 = b975
let c2 = round(c2,3)
x3label
xlimits 0.45 0.55
xtic mark decimal 2
x2label b025 = ^a1,  b975 = ^a2
histogram y1
x2label b025 = ^b1,  b975 = ^b2
histogram y2
x2label b025 = ^c1,  b975 = ^c2
histogram y3
x2label
title size
label size
tic label size
end of multiplot
. Finished Step 4.1: Page Back for Output

. Starting Step 5.1
.
summary y
. Finished Step 5.1: Page Back for Output

. Starting Step 5.2
.
let n = size y
let ymean = mean y
let ysdm = standard deviation of mean y
let idf = n - 1
.
let lclm = ymean - tppf(0.975,idf)*ysdm
let uclm = ymean + tppf(0.975,idf)*ysdm
.
let x = sequence 1 1 n
fit y x
let idf2 = n - 2
read dpst1f.dat coef coefsd
let bsd = coefsd(2)
let lclb = bsd - tppf(0.975,idf2)*bsd
let uclb = bsd + tppf(0.975,idf2)*bsd
let string idrift = NO
let atemp = lclb*uclb
if atemp < 0
  let string idrift = YES
end of if
.
. Finished Step 5.2: Page Back for Output

. Starting Step 5.3
.
let n = size y
let ysd = standard deviation y
let idf = n - 1
.
let ucls = idf*ysd*ysd/chsppf(0.025,idf)
let ucls = sqrt(ucls)
let lcls = idf*ysd*ysd/chsppf(0.975,idf)
let lcls = sqrt(lcls)
.
let x = sequence 1 1 n
let x = code4 x
levene test y x
.
. Finished Step 5.3: Page Back for Output

. Starting Step 5.4
.
runs y
.
y1label autocorrelation
x1label lag
let nlag = 20
xlimits 0 20
autocorrelation plot y
xlimits
let yauto = yplot(2)
let string irand = YES
let amin = maximum yplot subset tagplot = 4
let amax = maximum yplot subset tagplot = 3
if yauto < amin
  let string irand = NO
end of if
if yauto > amax
  let string irand = NO
end of if
y1label
x1label
.
. Finished Step 5.4: Page Back for Output

. Starting Step 5.5
.
set anderson darling critical value simulation
set goodness of fit fully specified off
.
let ksloc = mean y
let ksscale = sd y
normal anderson-darling goodness of fit test y
let string inormad = YES
if statval > cutoff95
  let string inormad = NO
end of if
let adstatn = statval
.
uniform mle y
let a = lowlimit
let b = upplimit
uniform anderson-darling goodness of fit test y
let string iunifad = YES
if statval > cutoff95
  let string iunifad = NO
end of if
let adstatu= statval
.
normal probability plot y
let NPPCC = PPCC
if NPPCC < .987
  let string inorm = NO
end of if
let string iunif = YES
uniform probability plot y
let UPPCC = PPCC
if UPPCC < .99
  let string iunif = NO
end of if
.
. Finished Step 5.5: Page Back for Output

. Starting Step 5.6
.
capture report.tex
print " "
print " "
print "Analysis for 500 uniform random numbers"
print " "
print "1: Sample Size                           = ^n"
print " "
print "2: Location"
print "   Mean                                  = ^ymean"
print "   Standard Deviation of Mean            = ^ysdm"
print "   95% Confidence Interval for Mean      = (^lclm,^uclm)"
print "   Drift with respect to location?       = ^idrift"
print " "
print "3: Variation"
print "   Standard Deviation                    = ^ysd"
print "   95% Confidence Interval for SD        = (^lcls,^ucls)"
print "   Drift with respect to variation?"
print "   (based on Levene's test on quarters"
print "   of the data)                          = NO"
print " "
print "4: Distribution"
print "   Normal PPCC                           = ^NPPCC"
print "   Normal Anderson-Darling               = ^UPPCC"
print "   Data are Normal?"
print "     (as tested by Normal PPCC)          = ^inorm"
print "     (as tested by Anderson-Darling)     = ^inormad"
print " "
print "   Uniform PPCC                          = ^UPPCC"
print "   Uniform Anderson-Darling              = ^iunifad"
print "   Data are Uniform?"
print "     (as tested by Uniform PPCC)         = ^iunif"
print "     (as tested by Anderson-Darling)     = ^iunifad"
print " "
print "5: Randomness"
print "   Autocorrelation                       = ^yauto"
print "   Data are Random?"
print "     (as measured by autocorrelation)    = ^irand"
print " "
print "6: Statistical Control"
print "   (i.e., no drift in location or scale,"
print "   data is random, distribution is "
print "   fixed, here we are testing only for"
print "   fixed uniform)"
print "   Data Set is in Statistical Control?   = YES"
print " "
end of capture
list report.tex
. Finished Step 5.6: Page Back for Output