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Re: Gaps in plotted graph, probably resulting from real values being miscomputed as complex

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123508] Re: Gaps in plotted graph, probably resulting from real values being miscomputed as complex
  • From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
  • Date: Fri, 9 Dec 2011 05:57:19 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On Thu, 08 Dec 2011 10:25:11 -0000, jdm <james.d.mclaughlin at gmail.com>  
wrote:

> Plot[Log[2,
>   PDF[NormalDistribution[0, 1],
>     InverseCDF[NormalDistribution[0, 1], (1 - 2^(-x))]]^2], {x, 1,
>   256}, PlotRange -> {-500, 0}]
>
> plots up to about x=56, and then nothing.
>
> Based on similar behaviour under another system, I suspect that some  
> sort of
> calculation error as 1 - 2^(-x) approaches 1 is causing some of the
> values that should be plotted to be wrongly computed as complex
> numbers, but have no way of confirming this and don't understand why
> the real-valued values aren't being plotted for their corresponding x
> if this is the case.
>
> Can anyone suggest anything?
>
> Thanks,
>
> James McLaughlin.
>

Working in machine precision without precision tracking leads to numerical  
errors in this case. Switching on precision tracking fixes the issue:

Plot[
  Log[2,
   PDF[
     NormalDistribution[0, 1],
     InverseCDF[NormalDistribution[0, 1], (1 - 2^(-x))]
    ]^2
  ], {x, 1, 256},
  PlotRange -> {-500, 0}, WorkingPrecision -> $MachinePrecision
]



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