Re: Area Under Curve (Min Length Interval)

• To: mathgroup at smc.vnet.net
• Subject: [mg53920] Re: Area Under Curve (Min Length Interval)
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 4 Feb 2005 04:11:15 -0500 (EST)
• Organization: The University of Western Australia
• References: <ctqdm2\$sd3\$1@smc.vnet.net> <ctrn6s\$bq8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <ctrn6s\$bq8\$1 at smc.vnet.net>, "Ray Koopman" <koopman at sfu.ca>
wrote:

> The minimum-length interval has equal densities at its endpoints.
>
> Needs["Statistics`"]
> F[x_] := CDF[ChiSquareDistribution[5],x]
> f[x_] := PDF[ChiSquareDistribution[5],x]
> FindRoot[{F[b]-F[a]==.93,f[b]==f[a]},{{a,1},{b,10}}]
> {F[b]-F[a],f[b]-f[a]}/.%
>
> {a->0.37253, b->10.3441}
> {0.93, 3.46945*^-18}

Amusingly, for this distribution, one can solve for the equal density
condition analytically,

sol = Solve[f[b] == f[a], a]

and then FindRoot,

FindRoot[F[b] - F[a] == 0.93 /. First[sol], {b, 10}]

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
The University of Western Australia      (CRICOS Provider No 00126G)
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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