V mnohych statistickych aplikaciach(IS, testy hypotez) sa stretneme so spojitymi rozdeleniami

Studentovo t rozdelenie

(χ^2)rozdelenie-rozdelenie kvadratickych foriem

Nakreslime krivky (hustoty ) tychto rozdeleni

Studentovo rozdelenie ma jeden parameter - pocet stupnov volnosti - n

st=StudentTDistribution[n]

PDF[st,x]

The Euler beta function
Beta[a,b] is Β(a,b)=Γ(a)Γ(b)/Γ(a+b)=(∫_0^1)(t^(a-1))(((1-t))^(b-1))dt.

Manipulate[Plot3D[Beta[a,b],{a,-n,n},{b,-n,n}],{n,1,5}]

densityST[n_,x_] := PDF[StudentTDistribution[n],x]

Do[gr[i]=Plot[densityST[i,t],{t,-5,5},PlotRange->All,PlotStyle->{Hue[0.3*i],Thickness[0.005]},Axes->{True,False}],{i,1,20}]

Show[Table[gr[i],{i,1,5}]]

Manipulate[gr[i]=Plot[densityST[i,t],{t,-5,5},PlotRange->All,PlotStyle->{Hue[0.3*i],Thickness[0.005]}],{i,1,20}]

Rozdelenie kvadratickych foriem ma jeden parameter - pocet stupnov volnosti

chi=ChiSquareDistribution[n]

PDF[chi,x]

TheEuler gamma function Gamma[z]is defined by the integralΓ(z)=(∫_0^∞)(t^(z-1))(e^(-t))dt.For positive integern,Γ(n)=(n-1)! .Γ(z)can be viewed as a generalization of the factorial function,valid for complex argumentsz.

Plot[Gamma[t],{t,-3,3}]

Manipulate[Plot[Gamma[t],{t,-n,5}],{n,1,5}]

densityCHI[n_,x_] := PDF[ChiSquareDistribution[n],x]

Do[grr[i]=Plot[densityCHI[i,t],{t,0,10},PlotStyle->{Hue[0.3*i],Thickness[0.005]}],{i,1,20}]

Show[Table[grr[i],{i,1,20}]]

Manipulate[grr[i]=Plot[densityCHI[i,t],{t,0,20},PlotStyle->{Hue[0.3*i],Thickness[0.005]}],{i,1,20}]