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.