Re: Solve for parameters of a truncated normal distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg122916] Re: Solve for parameters of a truncated normal distribution*From*: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>*Date*: Wed, 16 Nov 2011 04:44:58 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111151050.FAA23783@smc.vnet.net>

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.

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