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Solve for parameters of a truncated normal distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122903] Solve for parameters of a truncated normal distribution
  • From: paul <paulvonhippel at yahoo.com>
  • Date: Tue, 15 Nov 2011 05:50:44 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

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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