       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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