Re: Solve for parameters of a

*To*: mathgroup at smc.vnet.net*Subject*: [mg122957] Re: Solve for parameters of a*From*: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>*Date*: Fri, 18 Nov 2011 06:23:58 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111151050.FAA23783@smc.vnet.net>

I still like my animated Plot3D with the Opacity[0.5] plane. Go on, put that with your fancy matching coloured red variance and matching blue mean and your ViewPoint report, and you can have the pot! Barrie >>> On 18/11/2011 at 11:21 am, in message <op.v438ldxutgfoz2 at bobbys-imac.local>, DrMajorBob <btreat1 at austin.rr.com> wrote: > I'll meet that and raise you this: > > X = TruncatedDistribution[{0, \[Infinity]}, > NormalDistribution[\[Mu], \[Sigma]]]; > {mean, var} = FullSimplify@Through[{Mean, Variance}@X]; > > Manipulate[p = {3.3532, .2242, .3637}; > Column@{Row@{Style["variance = ", FontFamily -> "Arial", > FontSize -> 11.5, Red], > Style[ToString@height, FontFamily -> "Arial", FontSize -> 11.5], > Style[" = mean ", FontFamily -> "Arial", FontSize -> 11.5, > Blue]}, Show[{ContourPlot[ > mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, > ContourStyle -> {Red}, ImageSize -> 350], > ContourPlot[var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, > ContourStyle -> {Blue}]}, FrameLabel -> {"\[Mu]", "\[Sigma]"}], > Plot3D[{mean, var, 1}, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, > PlotStyle -> {Blue, Green, {Opacity[0.5], Gray}}, > ImageSize -> 350, ViewPoint -> Dynamic[p]], > ViewPoint -> Dynamic[p]}, {{height, 1}, 0.1, 3, 0.001}] > > Bobby > > On Thu, 17 Nov 2011 17:23:10 -0600, Barrie Stokes > <Barrie.Stokes at newcastle.edu.au> wrote: > >> Hi Bobby >> >> Very nice. My final mod of your mod of ... >> >> Manipulate[ >> Column@{Style[ >> "mean equals variance equals " <> >> ToString[height], FontFamily -> "Arial", FontSize -> 11.5], >> Show[{ContourPlot[ >> mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >> ContourStyle -> {Red}, ImageSize -> 350], >> ContourPlot[var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >> ContourStyle -> {Blue}]}, >> FrameLabel -> {"\[Mu]", "\[Sigma]"}], >> Plot3D[{mean, var, height}, {\[Mu], 0.01, 3}, {\[Sigma], >> 0.01, 3}, >> PlotStyle -> {Blue, Green, {Opacity[0.5], Gray}}, >> ImageSize -> 350]}, {{height, 1}, >> 0.1, 3, 0.001}] >> >> >> Best, >> >> Barrie >> >>>>> On 18/11/2011 at 6:19 am, in message >>>>> <op.v43um9zhtgfoz2 at bobbys-imac.local>, >> DrMajorBob <btreat1 at austin.rr.com> wrote: >>> Try this: >>> >>> X = TruncatedDistribution[{0, \[Infinity]}, >>> NormalDistribution[\[Mu], \[Sigma]]]; >>> {mean, var} = FullSimplify@Through[{Mean, Variance}@X]; >>> >>> Manipulate[ >>> p = {3.3532, .2242, .3637}; >>> Column@{Style[ >>> "mean can equal variance if contours intersect at height = " <> >>> ToString[height], FontFamily -> "Arial", FontSize -> 11.5], >>> Show[{ContourPlot[ >>> mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>> ContourStyle -> {Red}, ImageSize -> 350], >>> ContourPlot[var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>> ContourStyle -> {Blue}]}, FrameLabel -> {"\[Mu]", "\[Sigma]"}], >>> Plot3D[{mean, var, 1}, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>> PlotStyle -> {Blue, Green, Gray}, ImageSize -> 350, >>> ViewPoint -> Dynamic[p]], ViewPoint -> Dynamic[p]}, {{height, 1}, >>> 0.1, 3, 0.001}] >>> >>> I think the contour at 2 only adds confusion. >>> >>> Bobby >>> >>> On Thu, 17 Nov 2011 05:03:57 -0600, Barrie Stokes >>> <Barrie.Stokes at newcastle.edu.au> wrote: >>> >>>> Andrzej , Bobby >>>> >>>> Speaking of nice graphics: >>>> >>>> If you combine Bobby's mods to my ContourPlot ... >>>> >>>> X = TruncatedDistribution[{0, \[Infinity]}, >>>> NormalDistribution[\[Mu], \[Sigma]]]; >>>> {mean, var} = FullSimplify@Through[{Mean, Variance}@X]; >>>> Manipulate[ >>>> Column@{Style[ "contour height is " <> ToString[ height], >>>> FontFamily -> "Arial", FontSize -> 11.5 ], >>>> Show[{ContourPlot[ >>>> mean == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>>> ContourStyle -> {Red}, ImageSize -> 350], >>>> ContourPlot[var == height, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>>> ContourStyle -> {Blue}]}, >>>> FrameLabel -> {"\[Mu]", "\[Sigma]"}]}, {{height, 1}, 0.1, 3, >>>> 0.001}] >>>> >>>> with these plots from Andrzej's code (rotate both plots to reveal the >>>> "underside") ... >>>> >>>> X = TruncatedDistribution[{0, \[Infinity]}, >>>> NormalDistribution[\[Mu], \[Sigma]]]; >>>> m = Mean[X]; >>>> v = Variance[X]; >>>> >>>> and then ... >>>> >>>> Plot3D[{m, v, 1}, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>>> PlotStyle -> {Blue, Green, Gray}] >>>> >>>> and ... >>>> >>>> Plot3D[{m, v, 2}, {\[Mu], 0.01, 3}, {\[Sigma], 0.01, 3}, >>>> PlotStyle -> {Blue, Green, Gray}] >>>> >>>> the difference between height=1 and height=2 is clearly revealed. >>>> >>>> Cheers >>>> >>>> Barrie >>>> >>>> >>>> >>>> >>>>>>> On 16/11/2011 at 8:46 pm, in message >>>>>>> <201111160946.EAA06190 at smc.vnet.net>, >>>> Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: >>>> >>>>> On 15 Nov 2011, at 11:50, paul 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. >>>>>> >>>>>> >>>>> >>>>> Your first mistake is to use functions (Solve and NSolve) which are >>>>> not >>>>> intended for such purposes at all. NSolve can only solve (numerically) >>>>> polynomial equations and systems of such. Your equations are certainly >>>>> not of >>>>> this kind. Solve (in version 8) can also solve certain univariate >>>>> transcendental equations but not systems of such. So again, there is >>>>> no >>>>> point >>>>> at all of trying either of these functions on your system. >>>>> >>>>> The only function that might work is FindRoot. However, before one >>>>> even >>>>> starts, one has to have some reason for believing such a solution >>>>> exists. >>>>> Now, looking at the graphs below, I see no such reason. So do you have >>>>> one? >>>>> >>>>> X = TruncatedDistribution[{0, \[Infinity]}, >>>>> NormalDistribution[\[Mu], \[Sigma]]]; >>>>> >>>>> m = Mean[X]; >>>>> >>>>> v = Variance[X]; >>>>> >>>>> Plot3D[{m, v, 1}, {\[Mu], 0.1, 2}, {\[Sigma], 0.1, 2}, >>>>> PlotStyle -> {Blue, Green, Black}] >>>>> >>>>> Andrzej Kozlowski >>>> >>>> >>> >

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