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Re: Area Under Curve (Min Length Interval)


An exhaustive search seems better than NMinimize :

In[1]:=
<<Statistics`

In[2]:=
F[x_]:=CDF[ChiSquareDistribution[5],x];

In[3]:=
db=0.1;
bmax=b /. FindRoot[F[b] == 0.999,{b,10}]

Out[4]=
20.515

In[5]:=
First@Sort[
Table[{a,b,Abs[F[b]-F[a]-0.93]},{a,0,bmax,db},{b,a,bmax,db}]//
Flatten[#,1]&,#1[[3]]<#2[[3]]&]
Out[5]=
{1.3, 16.8, 0.0000365345}


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