Re: Solve for parameters of a truncated normal

*To*: mathgroup at smc.vnet.net*Subject*: [mg122936] Re: Solve for parameters of a truncated normal*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 17 Nov 2011 06:04:40 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111151050.FAA23783@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

That's a REALLY nice way to look at it... once all the code is given: X = TruncatedDistribution[{0, \[Infinity]}, NormalDistribution[\[Mu], \[Sigma]]]; {mean, var} = FullSimplify@Through[{Mean, Variance}@X]; Manipulate[ Column@{height, Show[{ContourPlot[ mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, ContourStyle -> {Red}], ContourPlot[var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, ContourStyle -> {Blue}]}, FrameLabel -> {"\[Mu]", "\[Sigma]"}]}, {{height, 1}, 0.1, 3, 0.001}] Bobby On Wed, 16 Nov 2011 03:44:58 -0600, Barrie Stokes <Barrie.Stokes at newcastle.edu.au> wrote: > Hi Paul > > I think this code: > > Manipulate[ > Show[ {ContourPlot[ > mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, > ContourStyle -> {Red} ], > ContourPlot[ var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, > ContourStyle -> {Blue} ]}, > FrameLabel -> {"\[Mu]", "\[Sigma]"} ], {{height, 1}, 0.1, 3, > 0.001} ] > > shows that this can't be done for the common value for the mean and > variance of 1. > > The minimum value for a solution is around 1.757 (after 30 seconds > playing with the above Manipulate). > > Cheers > > Barrie > >>>> On 15/11/2011 at 9:50 pm, in message >>>> <201111151050.FAA23783 at smc.vnet.net>, paul > <paulvonhippel at yahoo.com> wrote: >> I'm trying to solve the following problem: >> X = TruncatedDistribution[{0, \[Infinity]}, >> NormalDistribution[\[Mu], \[Sigma]]] >> Solve[Mean[X] == 1 && Variance[X] == 1, {\[Mu], \[Sigma]}, Reals] >> >> I get an error message: "This system cannot be solved with the methods >> available to Solve." It doesn't help if I replace Solve with NSolve. >> >> In case I've made a mistake in defining the problem, I should say that >> I'm looking for the parameters of a normal distribution so that, if >> the normal is truncated on the left at zero, the result will be a >> truncated distribution whose mean and variance are both 1. It seems to >> me Mathematica should be able to solve this, at least numerically. >> >> Many thanks for any suggestions. > > > -- DrMajorBob at yahoo.com

**References**:**Solve for parameters of a truncated normal distribution***From:*paul <paulvonhippel@yahoo.com>