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FindRoot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131634] FindRoot
  • From: bruce.colletti at gmail.com
  • Date: Sat, 14 Sep 2013 06:03:59 -0400 (EDT)
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Re 9.0.1 under Windows 7.

The code below is extracted from another source.

Part I below returns 289 even though n is never given a value.  Why does the module return a value and in particular, what does 289 mean?

Part II doesn't return a value (as expected).  I don't see why Part I returns a value but not Part II.

Thanks.

Bruce


In[1]:= 
(* Part I *)
f[n_,p1_,p2_]:=Sqrt[2n](ArcSin@Sqrt[p1-1/(2n)]-ArcSin@Sqrt[p2+1/(2n)]);

myModule1[\[Alpha]_,\[Beta]_]:=Module[{A=ConstantArray["",{9,9}],n,powerEST,p1=0.2,p2=0.1},
If[
p1>p2,
powerEST=SurvivalFunction[NormalDistribution[f[n,0.2,0.1],1],Quantile[NormalDistribution[],1-\[Alpha]]];

A[[IntegerPart[10(p1-0.1)],IntegerPart[10p2]]]=Ceiling[n/.FindRoot[powerEST-(1-\[Beta]),{n,40}]]
]
];

myModule1[0.05,0.05]
Out[3]= 289
In[4]:= 
(* Part II *)
myModule2[\[Alpha]_,\[Beta]_]:=Module[{A=ConstantArray["",{9,9}],n},
SurvivalFunction[NormalDistribution[f[n,0.2,0.1],1],Quantile[NormalDistribution[],1-\[Alpha]]]
];

myModule2[0.05,0.05]
Out[5]= 1/2 Erfc[(1.64485 -Sqrt[2] Sqrt[n$272] (ArcSin[Sqrt[0.2 -1/(2 n$272)]]-ArcSin[Sqrt[0.1 +1/(2 n$272)]]))/Sqrt[2]]



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