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
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