       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>

```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

```

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