       Re: Area Under Curve (Min Length Interval)

• To: mathgroup at smc.vnet.net
• Subject: [mg53901] Re: Area Under Curve (Min Length Interval)
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Wed, 2 Feb 2005 18:10:43 -0500 (EST)
• Organization: University of Washington
• References: <ctqdm2\$sd3\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Bruce,

One approach is to use a little calculus and FindRoot. Loading the
appropriate package, and defining F,

In:=
<<Statistics`ContinuousDistributions`
In:=
F[x_] := CDF[ChiSquareDistribution, x]

we find that

In:=
FindRoot[{F'[b]-F'[a]==0,F[b]-F[a]==93/100},{a,1},{b,5}]
Out=
{a -> 0.37253, b -> 10.3441}

Carl Woll

"Bruce Colletti" <vze269bv at verizon.net> wrote in message
news:ctqdm2\$sd3\$1 at smc.vnet.net...
> Re Mathematica 5.1.
>
> How would I compute the minimum length interval over which the area under
> f(x) is given?
>
> For instance, as shown below, f(x) is the PDF of a chi-square distributed
> random variable whose CDF is F[x].  Seeking the minimum length
> 93%-interval [a,b], the code returns "Obtained solution does not satisfy
> the following constraints within Tolerance -> 0.001..."  Fiddling with
> options has been futile.
>
> Any ideas?  Thankx.
>
> Bruce
>
> F[x_] := CDF[ChiSquareDistribution, x]
>
> Minimize[{b - a, F[b] - F[a] == 0.93, b > a > 0}, {a, b}]
>
> NMinimize[{b - a, F[b] - F[a] == 0.93, b > a > 0}, {a, b}]
>
>

```

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