Fig5_4-2.html

> restart:
read `C:\\Tanis-Hogg\\Maple Examples\\stat.m`:
read `C:\\Tanis-Hogg\\Maple Examples\\HistogramFill.txt`:
read `C:\\Tanis-Hogg\\Maple Examples\\ScatPlotCirc.txt`:
read `C:\\Tanis-Hogg\\Maple Examples\\ScatPlotPoint.txt`:
with(plots):

Elliot Tanis
June 12, 2006
Figures 5.4-2(a) and 5.4-2(b) (Fig5_4-2.mws)

Figures 5.4-2(a) and 5.4-2(b) Simulation of observations from an exponential distribution.

> randomize():

> for k from 1 to 1000 do
X := [seq(-ln(1 - rng()), k = 1 .. 16)]:
TT[k] := (Mean(X) - 1)/(StDev(X)/4):
od:
T := [seq(TT[k], k = 1 .. 1000)]:

> tbar := Mean(T);

> s := StDev(T);

> Min(T), Max(T);

> xtics := [seq(-7 + k*0.5, k = 0 .. 21)]:
ytics := [seq(0.05*k, k = 1 .. 8)]:
P1 := HistogramFill(T, -6.5 .. 3.5, 20):
P2 := plot([[0,0],[0,0]], x = -6.5 .. 3.5, y = 0 .. 0.41, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]):
display({P1, P2});

Similar to Figure 5.4-2(a)

>    #zper := [seq(NormalP(0, 1, k/1001), k = 1 .. 1000)]:
k := 'k':
for k from 1 to 500 do
  zp[k] := NormalP(0, 1, k/1001):
  zp[1000-k+1] := -zp[k]:
od:

> zper := [seq(zp[k], k = 1 .. 1000)]:

> Torder := sort(T):

> ScatPlotPoint(Torder, zper);

Similar to Figure 5.4-2(b)

>

> X := [seq(-ln(1 - rng()) + 9, k = 1 .. 16)];
Mean(X);
StDev(X);

The above are newly generated data. The following are those data in the text. We use the following at this time.

> X := [11.9776, 9.3889, 9.9798, 13.4676, 9.2895, 10.1242, 9.5798, 9.3148, 9.0605, 9.1680, 11.0394, 9.1083, 10.3720, 9.0523, 13.2969, 10.5852];

> xbar := Mean(X);
sx := StDev(X);

> probs := [seq(1/16, k = 1 .. 16)];
empPDF := zip((x,y)->(x,y),X,probs);

> for k from 1 to 1000 do
XX := DiscreteS(empPDF, 16):
TT[k] := (Mean(XX) - 10.3003)/(StDev(XX)/4):
od:
Tre := [seq(TT[k], k = 1 .. 1000)]:
tbar := Mean(Tre);
s := StDev(Tre);
Min(Tre), Max(Tre);

> xtics := [seq(-6.5+0.5*k, k = 0 .. 20)]:
ytics := [seq(0.05*k, k = 1 .. 8)]:

> P1 := HistogramFill(Tre, -6.5 .. 3.5, 20):
P2 := plot([[0,0],[0,0]], x=-6.5 .. 3.5, y = 0 .. 0.445, xtickmarks=xtics, ytickmarks=ytics, labels=[``,``]):
display({P1, P2});