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Re: Solve for parameters of a truncated normal distribution
*To*: mathgroup at smc.vnet.net
*Subject*: [mg122939] Re: Solve for parameters of a truncated normal distribution
*From*: Ray Koopman <koopman at sfu.ca>
*Date*: Thu, 17 Nov 2011 06:05:13 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <j9tga2$n91$1@smc.vnet.net> <ja00qu$62s$1@smc.vnet.net>
On Nov 16, 1:47 am, Ray Koopman <koop... at sfu.ca> wrote:
> On Nov 15, 2:52 am, paul <paulvonhip... 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.
>
> See "Left truncated normal distribution",
> https://groups.google.com/group/sci.stat.math/msg/374148b83b1b73f5
If I had re-familiarized myself with the message I that I provided a
link to, I would have pointed out that equation 8 there implies that
the desired condition, m = s, is attainable only if M/S = -Infinity.
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