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) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul