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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 19 "# Cauchy-Verteilung" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 50 "# LQ-Test zu vorgegebenem Siginifikanzniveau a
lpha" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "f0:=x->1/(Pi*(1+x^2));        # Dichte unter H0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "f1:=x->1/(Pi*(1+(x-mu)^2)); \+
  # Dichte unter H1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "q:=x
->f1(x)/f0(x);            # Likelihood-Quotient" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "q(mu/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "q_strich:=x->diff(q(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "y:=solve(q_strich(x)=0,x);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 5 "y[1];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "
y[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "q(y[1]);" }}}
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> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "c:=2.0;                  # LQ-Test zur Konstanten c" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=solve(q(x)=c);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a[1];" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "a[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 58 "int(f0(x),x=a[1]..a[2]); #Irrtumswahrscheinlichkeit 1. Art" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "int(f1(x),x=a[1]..a[2]); #Ma
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" {MPLTEXT 1 0 49 "# \"Klassischer\" Test zum Signifikanzniveau alpha:
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" 0 "" {MPLTEXT 1 0 12 "alpha:=0.05;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 79 "# Rechtes alpha-Quantil xr bei der Cauchy-Verteilung:
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44 "xr:=solve(int(f0(t),t=x..infinity)=alpha,x);" }}}{EXCHG {PARA 0 ">
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