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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: [mg123502] Re: Gaps in plotted graph, probably resulting from real values being miscomputed as complex
• From: Heike Gramberg <heike.gramberg at gmail.com>
• Date: Fri, 9 Dec 2011 05:56:13 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201112081022.FAA18861@smc.vnet.net>

This is because Plot uses WorkingPrecision->MachinePrecision by default. 
For x=56, 2^(-x) is about 1.4*10^-17. With a MachinePrecision of about 
16 this means that 1-2^(-x) is effectively 1. and therefore 
InverseCDF[=85] is effectively equal to Infinity for x>56. To plot the 
function for x>56 you could increase the working precision in Plot, e.g.


Plot[Log[2,
  PDF[NormalDistribution[0, 1],
    InverseCDF[NormalDistribution[0, 1], (1 - 2^(-x))]]^2], {x, 1,
  256}, PlotRange -> {-500, 0}, WorkingPrecision -> 100]

Heike

On 8 Dec 2011, at 11:22, jdm 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.
>

• References:
  • Gaps in plotted graph, probably resulting from real values being miscomputed as complex
    • From: jdm <james.d.mclaughlin@gmail.com>