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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.





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