Kombinatorik

> restart:

> 5!;

> binomial(12,10);

> binomial(a+3,a);

> expand(%);

> with(combinat);

Warning, the protected name Chi has been redefined and unprotected

> multinomial(12,5,5,2);

> 12! / (5! * 5! *2!);

> choose( [a,b,b,c]), numbcomb( [a,b,b,c]);

> choose( [a,b,b,c],2), numbcomb( [a,b,b,c], 2);

> randcomb( [a,b,b,c],2);

> permute([a,b,b,c]), numbperm([a,b,b,c]);

> permute([a,b,b,c],2), numbperm([a,b,b,c],2);

> randperm([a,b,b,c]);

> cproc:=cartprod( [[a,b,c],[x,y],[1,2]]):

> l:=[]: while not cproc[finished] do l:=[op(l),cproc[nextvalue]()]: od: l;

> partition(6), numbpart(6);

> composition(6,2), numbcomp(6,2);

Werkzeuge zur beschreibenden Statistik

> restart:with(stats): with(describe):

> data:=[ 2,3,4,Weight(5,4),missing,Weight(1..4,3) ];

> mean(data), (2+3+4+5*4+(1+4)/2*3)/10;

> importdata("c:\\kofler\\cd_neu_d\\R6\\Examples\\part3\\statdata.dat");

> importdata("c:\\kofler\\cd_neu_d\\R6\\Examples\\part3\\statdata.dat",3);

> with(transform):

Warning, the protected name apply has been redefined and unprotected

> tst:=[Weight(1..3,4), 3..4, Weight(4..7,4), 8];

> statvalue(tst);

> classmark(tst), statvalue(classmark(tst));

> frequency(tst), cumulativefrequency(tst);

> apply[sin](tst);

> multiapply[(x,y)->x*y]([[1,2,3], [4,5,6]]);

> scaleweight[1/count(tst)](tst);

> statsort( [6,missing,3,Weight(4..5,2)] );

> split[3]([1,2,3,4,5,6]);

> split[4]([1,2,3,4,5,6]);

> tallyinto( [1,2,2,2,3,4,5,6,6], [1..3,3..4,4..7]);

> tst:=[seq(rand(100)(), n=1..100)];

> bins:=[seq(10*n..10*n+10 ,n=0..9)];

> tallyinto(tst,bins);

> frequency(%);

Datenanalyse

> restart:with(stats): with(describe);

> tst:= [1,2,3,Weight(4..6,2),Weight(missing,2)]:

> count(tst), countmissing(tst);

> range(tst);

> mean(tst);

> quadraticmean(tst);

> standarddeviation(tst), variance(tst);

> quantile[3/4](tst), quartile[3](tst),percentile[75](tst);

> tst:=[1,2,3,4],[2,4,5,6]:

> linearcorrelation(tst ); evalf(%);

> covariance(tst); evalf(%);

Grafische Darstellung

> restart:

> with(stats): with(statplots): with(transform):

> with(random): with(describe): with(plots):

Warning, the protected name apply has been redefined and unprotected

Warning, the name poisson has been redefined

Warning, the name changecoords has been redefined

> f:=normald[5,1]: data:=[f(100)]:

> tallyinto(data, [seq(n*0.5..(n+1)*0.5,n=1..20)]):

> histdata:=scaleweight[1./count(%)](%);

> p1:=histogram(histdata,color=green):

> fpdf:=statevalf[pdf,f]:

> p2:=plot(fpdf(x), x=0.5..10):

> display( [p1, p2] );

> matrixplot( [[1,2,3], [3,4,5]], heights=histogram, axes=framed, gap=0.2, style=patch, shading=none, ambientlight=[0.5,0.5,0.5], light=[45,45,0.5, 0.5, 0.5]);

> datax:=[normald[5,1](100)]:

> datay:=[normald[7,2](100)]:

> scatterplot(datax,datay,color=navy);

> scatterplot(datax,datay,format=quantile);

> scatterplot(datax);

> scatterplot(datax,format=jittered);

> scatterplot([1, 2$5, 3$3,4$10, 5, 6$4],format=stacked);

> boxplot(datax);

> boxplot(datax,format=notched,shift=5,width=2);

> p1:=scatterplot(datax, datay):

> p2:=xyexchange(boxplot(datax,shift=18,width=1)):

> p3:=boxplot(datay,format=notched,shift=8,width=0.5):

> display( [p1,p2,p3] , view=[0..9,0..19]);

>

> yscale := (scl,x)-> xyexchange(xscale(scl,xyexchange(x))):

> tallyinto(datay, [seq(n..n+1, n=-2..18)]):

> histdata:=scaleweight[1./count(%)](%):

> p1:=histogram(histdata):

> p2:=yshift(0.3,yscale(0.05,scatterplot(datay,format=jittered))):

> display([p1,p2], axes=boxed);

Diskrete und stetige Verteilungen

> restart:with(stats): with(statevalf):

> f1:=statevalf[pdf,normald[0,1]]:

> f2:=statevalf[cdf,normald[0,1]]:

> f3:=statevalf[icdf,normald[0,1]]:

> f1(1), f2(1), f3(0.841);

> f3(f2(3));

> plot({f1(x), f2(x)}, x=-4..4);

> plot(f3(x),x=0..1, -3..3);

> statevalf[icdf,normald[90000,20000]](0.8);

> f1:=statevalf[pdf,exponential[1]]:

> plot(f1(x), x=0..4);

> f1:=statevalf[pdf,lognormal]:

> plot(f1(x), x=0..4);

> f1:=statevalf[pf,poisson[5]]:

> seq(f1(n), n=1..10);

> plot(f1(floor(x)), x=1..10,numpoints=1000);

Zufallszahlen

> restart:

> with(stats): with(random): with(statplots): with(plots): with(statevalf):

Warning, the name poisson has been redefined

Warning, the name changecoords has been redefined

> normald[10,1](3);

> f:=normald[10,1](generator[20]):

> f(), f(), f();

> yscale := (scl,x)-> xyexchange(xscale(scl,xyexchange(x))):

> f:=normald[5,2]:

> p1:=plot( statevalf[pdf,f](x), x=-2..12):

> p2:=yshift(0.2,yscale(0.03,scatterplot( [f(300)],format=jittered ))):

> display([p1,p2]);

> f:=beta[5,2]:

> p1:=plot( statevalf[pdf,f](x), x=0..1):

> p2:=yshift(2.6,yscale( 0.2,scatterplot([f(300)],format=jittered ))):

> display([p1,p2]);

>