Re: Solve for parameters of a truncated normal distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg122917] Re: Solve for parameters of a truncated normal distribution*From*: Paul von Hippel <paulvonhippel at yahoo.com>*Date*: Wed, 16 Nov 2011 04:45:08 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111151050.FAA23783@smc.vnet.net> <4EC38F2B.813B.006A.0@newcastle.edu.au>*Reply-to*: Paul von Hippel <paulvonhippel at yahoo.com>

Thanks, Barrie! You're the third person to suggest it can't be done. It surprises me, but I'm starting to believe it. Your demonstration has exceptionally spiffy graphics. I think you can push the common mean and variance of the truncated variablebelow 1.75 -- if you allow mu to be negative. For example, the common mean and variance of the truncated variable is 1.15 if {\[Mu] -> -7.37968, \[Sigma] -> 3.39052}. And if you don't require the mean and variance of the truncated variable to be equal, you can get even closer to mean=variance=1. E.g., FindRoot[{Mean[X] == 1.1, Variance[X] == 1}, {\[Mu], 1, -20, 6}, {\[Sigma], 2, 1, 10}] ________________________________ From: Barrie Stokes <Barrie.Stokes at newcastle.edu.au> To: mathgroup at smc.vnet.net; paul <paulvonhippel at yahoo.com> Sent: Tuesday, November 15, 2011 5:23 PM Subject: [mg122917] Re: [mg122903] Solve for parameters of a truncated normal distribution 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.

**References**:**Solve for parameters of a truncated normal distribution***From:*paul <paulvonhippel@yahoo.com>